PUBLICATIONS of KÁROLY
BÖRÖCZKY, Jr.
- K. Böröczky, Jr.:
Konvex testek approximációja poliéderekkel.
ps.gz
(in Hungarian) preprint.
- K. Ball, K.J. Böröczky:
Stability of the Prékopa-Leindler inequality.
pdf, submitted.
- K.J. Böröczky, E. Makai, M. Meyer, S. Reisner:
Volume product in the plane - lower estimates with stability.
pdf, submitted.
- K. Ball, K.J. Böröczky:
Stability of some versions of the Prékopa-Leindler inequality.
pdf, Monatshefte Math., accepted.
- K.J. Böröczky, F. Fodor, D. Hug:
The mean width of random polytopes circumscribed around a convex body.
pdf Journal of LMS, accepted.
- K.J. Böröczky, B. Csikós:
A new version of L. Fejes Tóth's Moment Theorem.
pdf Studia Sci. Hung., accepted.
- K.J. Böröczky; R. Schneider:
Mean width of circumscribed random polytopes.
pdf, Canadian Math. Bull., accepted.
- K.J. Böröczky:
Stability of the Blaschke-Santaló
and the affine isoperimetric inequalities.
pdf Advances in Mathematics, accepted.
- K. Böröczky, Jr.:
Parkettázások, elhelyezések
és fedések a hiperbolikus térben.
pdf
(in Hungarian), Matematikai Lapok, accepted.
- K. Böröczky, Jr.: Toric varieties and continued fractions,
In: Combinatorial Convex Geometry and Toric Varieties,
(G. Ewald, B. Teissier eds.). Birkhäuser, accepted.
- K. Böröczky, Jr.: Valuations and the combinatorial
Riemann-Roch theorem,
In: Combinatorial Convex Geometry and Toric Varieties,
(G. Ewald, B. Teissier eds.). Birkhäuser, accepted.
- 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.