[BOOK][B] Geometry of isotropic convex bodies

S Brazitikos, A Giannopoulos, P Valettas, BH Vritsiou - 2014 - books.google.com
The study of high-dimensional convex bodies from a geometric and analytic point of view,
with an emphasis on the dependence of various parameters on the dimension stands at the …

Chord measures in integral geometry and their Minkowski problems

E Lutwak, D **, D Yang, G Zhang - Communications on Pure …, 2024 - Wiley Online Library
To the families of geometric measures of convex bodies (the area measures of Aleksandrov‐
Fenchel‐Jessen, the curvature measures of Federer, and the recently discovered dual …

The logarithmic Minkowski problem

K Böröczky, E Lutwak, D Yang, G Zhang - Journal of the American …, 2013 - ams.org
The logarithmic Minkowski problem Page 1 JOURNAL OF THE AMERICAN MATHEMATICAL
SOCIETY Volume 26, Number 3, July 2013, Pages 831–852 S 0894-0347(2012)00741-3 …

Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

Y Huang, E Lutwak, D Yang, G Zhang - 2016 - projecteuclid.org
A longstanding question in the dual Brunn–Minkowski theory is “What are the dual
analogues of Federer's curvature measures for convex bodies?” The answer to this is …

[HTML][HTML] The log-Brunn–Minkowski inequality

KJ Böröczky, E Lutwak, D Yang, G Zhang - Advances in Mathematics, 2012 - Elsevier
For origin-symmetric convex bodies (ie, the unit balls of finite dimensional Banach spaces) it
is conjectured that there exist a family of inequalities each of which is stronger than the …

Lp dual curvature measures

E Lutwak, D Yang, G Zhang - Advances in Mathematics, 2018 - Elsevier
A new family of geometric Borel measures on the unit sphere is introduced. Special cases
include the L p surface area measures (which extend the classical surface area measure of …

[HTML][HTML] The logarithmic Minkowski problem for polytopes

G Zhu - Advances in Mathematics, 2014 - Elsevier
The logarithmic Minkowski problem asks for necessary and sufficient conditions for a finite
Borel measure on the unit sphere so that it is the cone-volume measure of a convex body …

[HTML][HTML] On the Lp dual Minkowski problem

Y Huang, Y Zhao - Advances in Mathematics, 2018 - Elsevier
The L p dual curvature measure was introduced by Lutwak, Yang & Zhang in an attempt to
unify the L p Brunn–Minkowski theory and the dual Brunn–Minkowski theory. The …

Existence of solutions to the even dual Minkowski problem

Y Zhao - Journal of Differential Geometry, 2018 - projecteuclid.org
Recently, Huang, Lutwak, Yang & Zhang discovered the duals of Federer's curvature
measures within the dual Brunn–Minkowski theory and stated the “Minkowski problem” …

The centro-affine Minkowski problem for polytopes

G Zhu - Journal of Differential Geometry, 2015 - projecteuclid.org
THE CENTRO-AFFINE MINKOWSKI PROBLEM FOR POLYTOPES Guangxian Zhu Abstract 1.
Introduction The setting for this paper is n-dimensi Page 1 j. differential geometry 101 (2015) …