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 …

[CITATION][C] Fourier Analysis in Convex Geometry

A Koldobsky - American Mathematical Society, 2005 - books.google.com
The study of the geometry of convex bodies based on information about sections and
projections of these bodies has important applications in many areas of mathematics and …

General affine isoperimetric inequalities

C Haberl, FE Schuster - Journal of Differential Geometry, 2009 - projecteuclid.org
GENERAL Lp AFFINE ISOPERIMETRIC INEQUALITIES Christoph Haberl & Franz E.
Schuster Abstract 1. Introduction Projection bodies Page 1 j. differential geometry 83 (2009) …

A classification of SL (n) invariant valuations

M Ludwig, M Reitzner - Annals of Mathematics, 2010 - JSTOR
A classification of upper semicontinuous and SL (n) invariant valuations on the space of n-
dimensional convex bodies is established. As a consequence, complete characterizations of …

The even Orlicz Minkowski problem

C Haberl, E Lutwak, D Yang, G Zhang - Advances in Mathematics, 2010 - Elsevier
The even Orlicz Minkowski problem Page 1 Advances in Mathematics 224 (2010) 2485–2510
www.elsevier.com/locate/aim The even Orlicz Minkowski problem Christoph Haberl, Erwin …

[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 …

Orlicz centroid bodies

E Lutwak, D Yang, G Zhang - Journal of Differential Geometry, 2010 - projecteuclid.org
The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a
star body (from below) by the volume of the star body itself is the Busemann-Petty centroid …

Orlicz projection bodies

E Lutwak, D Yang, G Zhang - Advances in Mathematics, 2010 - Elsevier
Minkowski's projection bodies have evolved into Lp projection bodies and their asymmetric
analogs. These all turn out to be part of a far larger class of Orlicz projection bodies. The …