PREPRINTS by KÁROLY J BÖRÖCZKY

• K.J. Böröczky, A. Figalli, Joao P.G. Ramos: The Isoperimetric inequality, the Brunn-Minkowski theory and Minkowski type Monge-Ampere equations on the sphere. pdf, manuscript, to be published by EMS Press

• K.J. Böröczky, Alexey Glazyrin: Stability of optimal spherical codes. pdf, submitted.

• K.J. Böröczky, A. De: Stability of the log-Brunn-Minkowski inequality in the case of many hyperplane symmetries. arxiv:2101.02549

PUBLICATIONS of KÁROLY J BÖRÖCZKY

• K.J. Böröczky, G. Lugosi, M. Reitzner: Facets of high-dimensional Gaussian polytopes. J. Geom. Anal. 34 (2024), no. 3, Paper No. 69. arxiv:1808.01431

• K.J. Böröczky, Danylo, Radchenko, Joao P.G. Ramos: A quantitative stability result for the sphere packing problem in dimensions 8 and 24. J. Reine Angew. Math. 808 (2024), 241-270. arXiv:2303.07908

• Ferenc Bartha, Ferenc Bencs, K.J. Böröczky, Daniel Hug: Extremizers and stability of the Betke-Weil inequality. Michigan Math. J. 74 (2024), 45-71. arxiv:2103.11672

• K.J. Böröczky: The logarithmic Minkowski conjecture and the Lp-Minkowski problem. Harmonic analysis and convexity, Adv. Anal. Geom., 9, De Gruyter, Berlin, 2023, 83-118. arxiv:2210.00194

• K.J. Böröczky, Pavlos Kalantzopoulos, Dongmeng Xi: The case of equality in geometric instances of Barthe's reverse Brascamp-Lieb inequality. Geometric aspects of functional analysis, Lecture Notes in Math., 2327, Springer, Cham, 2023, 129-165. arxiv:2203.01428

• K.J. Böröczky, Ádám Sagmeister: Stability of the isodiametric problem on the sphere and in the hyperbolic space. Adv. in Appl. Math. 145 (2023), Paper No. 102480, 49 pp. arxiv:2207.03043

• K.J. Böröczky, Ádám Sagmeister: Convex bodies of constant width in spaces of constant curvature and the extremal area of Reuleaux triangles. Studia Sci. Math. Hungar. 59 (2022), no. 3-4, 244-273. arxiv:2203.16636

• K.J. Böröczky, Daniel Hug: Reverse Alexandrov-Fenchel inequalities for zonoids. Commun. Contemp. Math. 24 (2022), no. 8, Paper No. 2150084, 32 pp. arxiv:2106.13143

• K.J. Böröczky, Pavlos Kalantzopoulos: Log-Brunn-Minkowski inequality under symmetry. Trans. Amer. Math. Soc. 375 (2022), no. 8, 5987-6013. arxiv:2002.12239

• K.J. Böröczky, A. De: Stable solution of the log-Minkowski problem in the case of hyperplane symmetries. J. Differential Equations 298 (2021), 298-322. arxiv:2101.03395

• K.J. Böröczky, A. De: Stability of the Prekopa-Leindler inequality for log-concave functions. Adv. Math. 386 (2021), Paper No. 107810, 42 pp. arxiv:2007.15304

• T. Bisztriczky, K. Böröczky, K.J. Böröczky: The T(5) property of packings of squares. Art Discrete Appl. Math. 4 (2021), no. 3, Paper No. 3.12, 11 pp. pdf.

• K.J. Böröczky, M. Domokos, G. Solanes: Dimension of the space of unitary equivariant translation invariant tensor valuations. J Func Anal, 280 (2021), no. 4, 108862. arxiv:2003.04649

• K.J. Böröczky, Daniel Hug: A reverse Minkowski-type inequality. Proc. AMS, 148 (2020), no. 11, 4907-4922. arxiv:1909.00782

• K.J. Böröczky, M. Matolcsi, I. Ruzsa, P. Santos, O. Serra: Triangulations and a discrete Brunn-Minkowski inequality in the plane. Disc. Comp. Geom., 64 (2020), 396-426. arxiv:1812.04117

• K.J. Böröczky, E. Lutwak, D. Yang, G. Zhang, Yiming Zhao: The Gauss image problem. pdf, Communications on Pure and Applied Mathematics, 73 (2020), 1406-1452.

• G. Bianchi, K.J. Böröczky, A. Colesanti: Smoothness in the Lp Minkowski problem for p< 1. pdf, Journal of Geometric Analysis, 30 (2020), 680-705.

• K.J. Böröczky, A. Sagmeister: Isodiametric problem on the sphere and in the hyperbolic space. Acta Math. Hungarica, 160 (2020), 13-32. arxiv:1812.09753

• G. Bianchi, K.J. Böröczky, A. Colesanti: The Orlicz version of the Lp dual Minkowski problem on Sn for n< p< 0. 111 (2019), 101937. arxiv:1812.05213

• K.J. Böröczky: The logarithmic Minkowski problem, the logarithmic Brunn-Minkowski conjecture and relatives. Oberwolfach Reports. OWR_2018_54 (2019), 29-20. conference's site

• J. Abardia, K.J. Böröczky, M. Domokos, D. Kertész: SL(m,C) equivariant and translation covariant continuous tensor valuations.Journal of Functional Analysis, 276 (2019), 3325-3362. pdf

• K.J. Böröczky, F. Fodor: The Lp dual Minkowski problem for p>1 and q>0. Journal of Differential Equations, 266 (2019), 7980-8033. arxiv:1802.00933

• K.J. Böröczky, F. Fodor, D. Hug: Strengthened volume inequalities for Lp zonoids of even isotropic measures. pdf, Trans. AMS, 371 (2019), 505-548.

• K.J. Böröczky, M. Ludwig: Minkowski valuations on lattice polytopes. pdf, JEMS, 21 (2019), 163-197.

• G. Bianchi, K.J. Böröczky, A. Colesanti: The Lp-Minkowski problem for -n< p<1 according to Chou-Wang. pdf, Adv. Math., 341 (2019), 493-535.

• K. Böröczky, K.J. Böröczky, Alexey Glazyrin, Ágnes Kovács: Stability of the simplex bound for packings by equal spherical caps determined by simplicial regular polytopes. In: M.D.E. Conder, A. Deza, A.I. Weiss (eds): Discrete Geometry and Symmetry. Volume in honor of K Bezdek's and E. Schulte's 60th birthday, Springer, 2018, 31-60. pdf,

• K.J. Böröczky, Á. Kovács: The isoperimetric problem for 3-polytopes with six vertices. Annales Universitatis Scientiarium Budapestinensis de Rolando Eötvös Nominatae Sectio Mathematica, 61 (2018), 55-67. pdf

• K.J. Böröczky, M. Henk, H. Pollehn: Subspace concentration of dual curvature measures. pdf, Journal of Differential Geometry, 109 (2018), 411-429.

• K.J. Böröczky, F. Fodor (eds): Volume honoring Ted Bisztriczki's, Gabor Fejes Toth's and Endre Makai's 70th birthday, Acta Mathematica Hungarica, 155 (2018).

• G. Ambrus, I. Bárány, K.J. Böröczky, G. Fejes Tóth, J. Pach (eds): New Trends in Intuitive Geometry. Bolyai Studies, Springer, 2018.

• K.J. Böröczky, M. Ludwig: Valuations on Lattice Polytopes. pdf, In:Tensor Valuations and their Applications in Stochastic Geometry and Imaging (M.~Kiderlen and E.~Vedel~Jensen, eds.), Springer Lecture Notes in Math 2177, (2017), 213-234.

• K.J. Böröczky, Hai T. Trinh: The planar Lp-Minkowski problem for 0&< p&< 1. pdf, Adv. Applied Mathematics, 87 (2017), 58-81.

• K.J. Böröczky, M. Henk: Cone volume measure and stability. pdf, Advances in Mathematics, 306 (2017), 24-50.

• K.J. Böröczky, D. Hug: Isotropic measures and stronger forms of the reverse isoperimetric inequality. pdf, Trans. AMS, 369 (2017), 6987-7019.

• K.J. Böröczky, P. Hegedűs, G. Zhu: On the discrete logarithmic Minkowski problem. pdf, IMRN, 6 (2016), 1807-1838.

• K.J. Böröczky, M. Henk: Cone volume measure of general centered convex bodies. pdf, Advances in Math., 289 (2016), 703-721.

• K.J. Böröczky, P. Hegedűs: The cone volume measure of antipodal points. pdf, Acta Math. Hung., 146 (2015), 449-465.

• K.J. Böröczky, E. Lutwak, D. Yang, G. Zhang: Affine images of isotropic measures. pdf, J. Diff. Geom., 99 (2015), 407-442.

• K.J. Böröczky, B. Hoffman: A note on triangulations of sum sets. pdf, Involve, 8 (2015), 75-85.

• K.J. Böröczky, F. Santos, O. Serra: On sumsets and convex hull. pdf, Disc. Comp. Geom., 52 (2014), 705-729.

• G. Ambrus, K.J. Böröczky: Stability results for the volume of random simplices. pdf, Amer. J. Math., 136 (2014), 833-857.

• F. Barthe, K.J. Böröczky, M. Fradelizi: Stability of the functional forms of the Blaschke-Santaló inequality. pdf, Monatshefte Math., 173 (2014), 135-159.

• I.Bárány, K.J. Böröczky, G. Fejes Tóth, J. Pach (eds): Geometry - Intuitive, Discrete, and Convex: A Tribute to László Fejes Tóth. BOLYAI SOCIETY MATHEMATICAL STUDIES, 24, Springer, 2013.

• K.J. Böröczky: Stronger versions of the Orlicz-Petty projection inequality. pdf, J. Diff. Geom., 95 (2013), 215-247.

• K.J. Böröczky, E. Makai, M. Meyer, S. Reisner: Volume product in the plane - lower estimates with stability. pdf, Studia Sci. Math. Hung., 50 (2013), 159-198.

• K.J. Böröczky, E. Lutwak, D. Yang, G. Zhang: The Logarithmic Minkowski Problem. pdf, Journal of the American Mathematical Society, 26 (2013), 831-852.

• K.J. Böröczky, F. Fodor, D. Hug: Intrinsic volumes of random polytopes with vertices on the boundary of a convex body. pdf , Transactions of AMS, 365 (2013), 785-809.

• K.J. Böröczky, P.P. Pálfy, O. Serra: On the cardinality of sumsets in torsion-free groups. pdf, Bull. LMS, 44 (2012), 1034-1041.

• K.J. Böröczky, Oriol Serra: Remarks on the equality case of the Bonnesen inequality. pdf, Archiv der Math., 99 (2012), 189-199.

• K.J. Böröczky, E. Lutwak, D. Yang, G. Zhang: The log-Brunn-Minkowski-inequality. pdf, Advances in Mathematics, 231 (2012), 1974-1997.

• C. Barvard, K.J. Böröczky, B. Ormos, I. Prok, L. Vena, G. Wintsche: Regularly triangulated hyperbolic surfaces. pdf, Acta Sci. Math. (Szeged), 77 (2011), 669-679.

• K. Ball, K.J. Böröczky: Stability of some versions of the Prékopa-Leindler inequality. pdf, Monatshefte Math., 163 (2011), 1-14.

• K. Böröczky, Jr.: Parkettázások, elhelyezések és fedések a hiperbolikus térben. pdf (in Hungarian), Matematikai Lapok, 16 (2010), 62-78.

• K.J. Böröczky, F. Fodor, D. Hug: The mean width of random polytopes circumscribed around a convex body. pdf Journal of LMS, 81 (2010), no. 2, 499-523.

• K. Ball, K.J. Böröczky: Stability of the Prékopa-Leindler inequality. pdf, Mathematika, 56 (2010), 339-356.

• K.J. Böröczky; R. Schneider: Mean width of circumscribed random polytopes. pdf, Canadian Math. Bull., 53 (2010), 614-628.

• K.J. Böröczky: Stability of the Blaschke-Santaló and the affine isoperimetric inequalities. pdf Advances in Mathematics, 225 (2010), 1914-1928.

• K.J. Böröczky, B. Csikós: A new version of L. Fejes Tóth's Moment Theorem. pdf Studia Sci. Hung., 47 (2010), 230-256.

• K.J. Böröczky, D. Hug: Stability of the inverse Blaschke-Santaló inequality for zonoids. Adv. Appl. Math., 44 (2010), 309-328. pdf

• K.J. Böröczky; R. Schneider: Stable determination of convex bodies from sections. pdf, Studia Sci. Math. Hung., 46 (2009), 367-376.

• K.J. Böröczky, B. Csikós: Approximation of smooth convex bodies by circumscribed polytopes with respect to the surface area. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, pdf 79 (2009), 229-264.

• K.J. Böröczky, F. Fodor, M. Reitzner, V. Vígh: Mean width of random polytopes in a reasonable smooth convex body. pdf, Journal of Multivariate Analysis, 100 (2009), 2287-2295.

• K.J. Böröczky, L. M. Hoffmann, D. Hug: Expectation of mean projections of inscribed random polytopes. pdf, Periodica Hungarica, 57 (2008), 143-164.

• K.J. Böröczky; R. Schneider: A characterization of the duality mapping for convex bodies. pdf, GAFA, 18 (2008), 657-667.

• K.J. Böröczky, F. Fodor, V. Vígh: Approximating 3-dimensional convex bodies by polytopes with a restricted number of edges. pdf , Beit. Alg. Geom, 49 (2008), 177-193.

• K. Böröczky; K.J. Böröczky; C. Schütt; G. Wintsche: Convex bodies of minimal volume, surface area and mean width with respect to thin shells. pdf Canadian Journal of Mathematics, 60 (2008), 3-32.

• K.J. Böröczky; Salvador S. Gomez; P. Tick: Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges. pdf , Monats. Math., 153 (2008), 23-48.

• K. Böröczky, Jr.; G. Wintsche: Extremal mean width when covering the one-skeleton. pdf . Bull. London Math. Soc., 39 (2007), 921-928.

• K.J. Böröczky, P. Tick, G. Wintsche: Typical faces of best approximating three-polytopes. pdf Beit. Alg. Geom, 48 (2007), 521-545.

• K. Böröczky, K.J. Böröczky: A stability property of the octahedron and the icosahedron . Publ. Math. Debrecen, 71 (2007), 449-466.

• K.J. Böröczky: Polytopal approximation of smooth convex bodies. pdf In: Konvexgeometrie, Oberwolfach Report No. 56/2006, 3351-3354, 2007.

• K.J. Böröczky; R. Schneider: Circumscribed Simplices of Minimal Mean Width. pdf Beit. Alg. Geom., 48 (2007), 217-224.

• K. Böröczky; K. Böröczky, Jr.: Polytopes of minimal volume with respect to a shell - another characterization of the octahedron and the icosahedron pdf . Disc. Comp. Geom., 38 (2007), 231-241.

• K. Böröczky, Jr., I.Z. Ruzsa: Note on an inequality of Wegner. pdf . Disc. Comp. Geom., 37 (2007), 245-249.

• K. Böröczky, Jr.; I. Fábián; G. Wintsche: Covering the crosspolytope by equal balls . Periodica Math. Hung., 53 (2006), 103-113.

• K. Böröczky; K. Böröczky, Jr., G. Wintsche: Typical faces of extremal polytopes with respect to a thin three-dimensional shell. . Periodica Math. Hung., 53 (2006), no. 1-2, 83-102.

• K.J. Böröczky; J. Pach; G. Tóth: Planar crossing numbers of graphs embeddable in another surface. pdf International Journal of Foundations of Computer Science, 17 (2006), 1005-1017.

• K. Böröczky, Jr.; T. Réti; G. Wintsche: On the combinatorial characterization of quasicrystals. pdf J. Geometry and Physics, 57 (2006), 39-52.

• U. Betke, K. Böröczky, Jr.: Finite lattice packings and the Wulff-shape . Mathematika, 52 (2005), 17-29.

• T. Réti, K. Böröczky, Jr.: Topological characterization of finite cellular systems represented by 4-dimensional polytopes. Materials Science Forum, 473--474 (2005), 381-388.

• K. Böröczky, Jr.: Finite coverings in the hyperbolic plane. Discrete and Computational Geometry, 33 (2005), 165-180.

• K. Böröczky, Jr.: The stability of the Rogers-Shepard inequality. Adv. Math., 190 (2005), 47-76.

• K. Böröczky, Jr., M. Reitzner: Approximation of Smooth Convex Bodies by Random Circumscribed Polytopes. Annals of Applied Prob., 14 (2004), 239-273.

• T. Bisztriczky, K. Böröczky, Jr., D.S. Gunderson: Cyclic polytopes, hyperplanes, and codes. J. Geometry, 78 (2003), 25-49.

• K. Böröczky, Jr.: Finite packing and covering by congruent convex domains. Discrete and Computational Geometry, 30 (2003), 185-193.

• K. Böröczky, Jr., J. Kollár, T. Szamuely (eds): Higher Dimensional Varieties and Rational Points. Springer-Verlag, 2003.

• K. Böröczky, Jr., G. Wintsche: Covering the sphere by equal spherical balls . In: Discrete and Computational Geometry, The Goodman-Pollack Festschrift, 237-253, 2003.

• K. Böröczky, Jr., M.A. Hernández Cifre, G. Salinas Martínez: Optimizing the perimeter and the area for convex sets for prescribed circumradius and inradius. Monats. Math., 138 (2003), 95-110.

• I. Bárány, K. Böröczky, Jr.: Lattice points on the boundary of the integer hull. In: (A. Bezdek, ed.), Discrete Geometry, Marcel Dekker, 2003, 33-48.

• T. Réti, K. Böröczky, Jr.: Topological characterization of 2D finite cellular system. Material Science Forum, 414-415 (2003), 471-482.

• K. Böröczky, Jr., G. Tardos: The longest segment in the complement of a packing . Mathematika, 49 (2002), 45-49.

• K. Böröczky, Jr., G. Fejes Tóth: Stability of some inequalities for three-polyhedra, Rend. Circ. Mat. Palermo, 70 (2002), 93-108.

• K. Böröczky, Jr.: Discrete point sets in the hyperbolic plane, Studia Sci. Math. Hung., 39 (2002), 21-36.

• T. Bisztriczky, K. Böröczky, Jr.: About the centroid body and the ellipsoid of inertia, Mathematika, 48 (2001), 1-13.

• T. Bisztriczky, K. Böröczky, Jr.: On periodically cyclic Gale 4-polytopes, Disc. Math., 241 (2001), 103-118.

• K. Böröczky: About the error term for best approximation with respect to the Hausdorff related metrics, Disc. Comp. Geom., 25 (2001), 293-309.

• V. Arhelger, U. Betke and K. Böröczky, Jr.: Large finite lattice packings, Geometriae Dedicata, 85 (2001), 157-182.

• K. Böröczky, Jr., G. Wintsche: Sphere packings in the regular crosspolytope, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 43 (2000), 151-157.

• K. Böröczky, Jr., D.G. Larman, S.Sezgin, C. Zong: On Generalized Kissing Numbers and Blocking Numbers, Rend. Circ. Mat. Palermo, 65 (2000), 39-57.

• T. Bisztriczky, K. Böröczky, Jr.: On the rigidity of multiplices, Disc. Comp. Geom., 24 (2000), 177-184.

• K. Böröczky: Approximation of general smooth convex bodies. Adv. Math., 153 (2000), 325-341.

• K. Böröczky: The error of polytopal approximation with respect to the symmetric difference metric and the L$_p$ metric, Isr. J. Math., 117. (2000), 1-28.

• K. Böröczky: Polytopal approximation bounding the number of $k$-faces., J. Approximation Th., 102 (2000), 283-285.

• K. Böröczky, Jr., U. Schnell, J.M. Wills: Quasicrystals, parametric density and Wulff-shape, In: Directions in Mathemathical Quasicrystals, eds. M. Baake, R.V. Moody, CRM Monographs Series 13, AMS, 2000, 259-276.

• K. Böröczky, Jr., M. Henk: Random Projections of Regular Polytopes , Arch. Math., 73. (1999), 465-473.

• K. Böröczky, Jr., W. Neumann, A. Stipsicz (eds): Low Dimensional Topology, J. Bolyai Series in Mathematics, Budapest, 1999.

• U. Betke, K. Böröczky, Jr.: Asymptotic formulae for the lattice point enumerator, Can. Jour. Math., 51. (1999), 225-249.

• K. Böröczky, Jr., M. Ludwig: Approximation of the 3-ball by polytopes, Monats. Math., 127. (1999), 101-110.

• K. Böröczky, Jr., U. Schnell: Quasi-Crystals and Wulff-shape, Disc. Comp. Geom., 21 (1999), 421-436.

• K. Böröczky, Jr., U. Schnell: Asymptotic shape of finite packings, Can. Jour. Math., 50 (1998), 16-28.

• K. Böröczky, Jr., U. Schnell: Wulff-shape for non-periodic arrangements, Letters Math. Phys., 45 (1998), 81-94.

• K. Böröczky, Jr.: Packings of four and five balls, In: Proceedings of the Conference on Intuitive Geometry, Budapest, (1997), 265-276.

• K. Böröczky, Jr.: Lattice points in large bodies, Rend. Circ. Mat. Palermo, 50 (1997), 67-76.

• K. Böröczky, Jr., J.M. Wills: Finite sphere packings and critical radii, Beit. Alg. Geom., 38 (1997), 193-211.

• K. Böröczky, Jr.: Around the Rogers-Shepard inequality, Mathematica Pannonica, 7 (1996), 113-130.

• K. Böröczky, Jr., V. Soltan: Smallest maximal snakes of translates of convex domains, Geometriae Dedicata, 54 (1995), 31-44.

• K. Böröczky, Jr., M. Henk: Radii and the Sausage Conjecture, Canadian Mathematical Bulletin, 38 (1995), 156-166.

• K. Böröczky, Jr.: Mean projections and finite packings of convex bodies, Monatshefte Math., 118 (1994), 41-54.

• K. Böröczky, Jr.: Some extremal properties of the regular simplex, In: Proceedings of the Conference on Intuitive Geometry, Szeged, (1994), 45-61.

• K. Böröczky, Jr.: About four-ball packings, Mathematika, 40 (1993), 226-232.

• K. Böröczky, Jr., N. Sauer and X. Zhu: Inexhaustible homogeneous structures, Discrete Mathematics, 115 (1993), 57-63.

• K. Böröczky, Jr.: About the mean width of simplices, Periodica Polytechnica, 40 (1992), 291-297.

• T. Bisztriczky, K. Böröczky, Jr., H. Harboth, L. Piepmeyer: On the smallest limited snake of unit disks, Geometriae Dedicata, 40 (1991), 319-324.

• K. Böröczky, Jr.: Rectangular convexity of convex domains of constant width, Geometriae Dedicata, 34 (1990), 13-84.