Inequalities for quermassintegrals on k-convex domains

Sun Yung Alice Chang; Yi Wang

doi:10.1016/j.aim.2013.08.006

Inequalities for quermassintegrals on k-convex domains

Sun Yung Alice Chang, Yi Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

In this paper, we study the Aleksandrov-Fenchel inequalities for quermassintegrals on a class of non-convex domains. Our proof uses optimal transport maps as a tool to relate curvature quantities of different orders defined on the boundary of the domain.

Original language	English (US)
Pages (from-to)	335-377
Number of pages	43
Journal	Advances in Mathematics
Volume	248
DOIs	https://doi.org/10.1016/j.aim.2013.08.006
State	Published - Nov 25 2013

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Aleksandrov-Fenchel quermassintegral inequalities
K-Convexity
Optimal transport maps

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10.1016/j.aim.2013.08.006

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title = "Inequalities for quermassintegrals on k-convex domains",

abstract = "In this paper, we study the Aleksandrov-Fenchel inequalities for quermassintegrals on a class of non-convex domains. Our proof uses optimal transport maps as a tool to relate curvature quantities of different orders defined on the boundary of the domain.",

keywords = "Aleksandrov-Fenchel quermassintegral inequalities, K-Convexity, Optimal transport maps",

author = "Chang, \{Sun Yung Alice\} and Yi Wang",

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T1 - Inequalities for quermassintegrals on k-convex domains

AU - Chang, Sun Yung Alice

AU - Wang, Yi

PY - 2013/11/25

Y1 - 2013/11/25

N2 - In this paper, we study the Aleksandrov-Fenchel inequalities for quermassintegrals on a class of non-convex domains. Our proof uses optimal transport maps as a tool to relate curvature quantities of different orders defined on the boundary of the domain.

AB - In this paper, we study the Aleksandrov-Fenchel inequalities for quermassintegrals on a class of non-convex domains. Our proof uses optimal transport maps as a tool to relate curvature quantities of different orders defined on the boundary of the domain.

KW - Aleksandrov-Fenchel quermassintegral inequalities

KW - K-Convexity

KW - Optimal transport maps

UR - https://www.scopus.com/pages/publications/84883529514

UR - https://www.scopus.com/inward/citedby.url?scp=84883529514&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2013.08.006

DO - 10.1016/j.aim.2013.08.006

M3 - Article

AN - SCOPUS:84883529514

SN - 0001-8708

VL - 248

SP - 335

EP - 377

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Inequalities for quermassintegrals on k-convex domains

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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