The dual Minkowski problem for symmetric convex bodies

Autor:	Böröczky, Károly, Lutwak, Erwin, Yang, Deane, Zhang, Gaoyong, Zhao, Yiming
Rok vydání:	2017
Předmět:	Mathematics - Metric Geometry Mathematics - Analysis of PDEs Mathematics - Differential Geometry 52A40
Druh dokumentu:	Working Paper
Popis:	The dual Minkowski problem for even data asks what are the necessary and sufficient conditions on an even prescribed measure on the unit sphere for it to be the $q$-th dual curvature measure of an origin-symmetric convex body in $\mathbb{R}^n$. A full solution to this is given when $1 < q < n$. The necessary and sufficient condition is an explicit measure concentration condition. A variational approach is used, where the functional is the sum of a dual quermassintegral and an entropy integral. The proof requires two crucial estimates. The first is an estimate of the entropy integral proved using a spherical partition. The second is a sharp estimate of the dual quermassintegrals for a carefully chosen barrier convex body. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.06259 Zobrazit plný text záznamu View this record from Arxiv