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- Publications
- Influence

The log-Brunn-Minkowski inequality

- K. Böröczky, E. Lutwak, Deane Yang, Gaoyong Zhang
- Mathematics
- 1 October 2012

Abstract For origin-symmetric convex bodies (i.e., 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… Expand

The logarithmic Minkowski problem

- K. Böröczky, E. Lutwak, Deane Yang, Gaoyong Zhang
- Mathematics
- 5 June 2012

In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a… Expand

L p Affine Isoperimetric Inequalities

- E. Lutwak, Deane Yang, Gaoyong Zhang
- Mathematics
- 2000

The Lp analogues of the Petty projection inequality and the BusemannPetty centroid inequality are established. An affine isoperimetric inequality compares two functionals associated with convex (or… Expand

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

- Y. Huang, E. Lutwak, Deane Yang, Gaoyong Zhang
- Mathematics
- 16 November 2016

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 provided. This leads naturally to… Expand

CONVOLUTIONS, TRANSFORMS, AND CONVEX BODIES

- Eric L. Grinberg, Gaoyong Zhang
- Mathematics
- 1999

The paper studies convex bodies and star bodies in $\Bbb R^n$ by using Radon transforms on Grassmann manifolds, $p$-cosine transforms on the unit sphere, and convolutions on the rotation group of… Expand

Sharp Affine LP Sobolev Inequalities

- E. Lutwak, Deane Yang, Gaoyong Zhang
- Mathematics
- 2002

In this paper we prove a sharp affine Lp Sobolev inequality for functions on R. The new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of… Expand

Orlicz projection bodies

- E. Lutwak, Deane Yang, Gaoyong Zhang
- Mathematics
- 15 January 2010

Abstract Minkowski's projection bodies have evolved into L p projection bodies and their asymmetric analogs. These all turn out to be part of a far larger class of Orlicz projection bodies. The… Expand

Centered bodies and dual mixed volumes

- Gaoyong Zhang
- Mathematics
- 1 February 1994

We establish a number of characterizations and inequalities for intersection bodies, polar projection bodies and curvature images of projection bodies in R" by using dual mixed volumes. One of the… Expand