Kotrbatý’s theorem on valuations and geometric inequalities for convex bodies

Semyon Alesker

doi:10.1007/s11856-021-2269-z

Kotrbatý’s theorem on valuations and geometric inequalities for convex bodies

Semyon Alesker

School of Mathematical Sciences

Tel Aviv University

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

Abstract

Very recently J. Kotrbatý[14] has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge-Riemann bilinear relations in Kähler geometry. The goal of this note is to prove several inequalities for mixed volumes of convex bodies using Kotrbatý’s theorem as the main tool.

Original language	English
Pages (from-to)	361-378
Number of pages	18
Journal	Israel Journal of Mathematics
Volume	247
Issue number	1
DOIs	https://doi.org/10.1007/s11856-021-2269-z
State	Published - Apr 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-021-2269-z

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title = "Kotrbat{\'y}{\textquoteright}s theorem on valuations and geometric inequalities for convex bodies",

abstract = "Very recently J. Kotrbat{\'y}[14] has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge-Riemann bilinear relations in K{\"a}hler geometry. The goal of this note is to prove several inequalities for mixed volumes of convex bodies using Kotrbat{\'y}{\textquoteright}s theorem as the main tool.",

author = "Semyon Alesker",

note = "Publisher Copyright: {\textcopyright} 2021, The Hebrew University of Jerusalem.",

year = "2022",

month = apr,

doi = "10.1007/s11856-021-2269-z",

language = "الإنجليزيّة",

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AU - Alesker, Semyon

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AB - Very recently J. Kotrbatý[14] has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge-Riemann bilinear relations in Kähler geometry. The goal of this note is to prove several inequalities for mixed volumes of convex bodies using Kotrbatý’s theorem as the main tool.

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DO - 10.1007/s11856-021-2269-z

M3 - مقالة

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VL - 247

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EP - 378

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Kotrbatý’s theorem on valuations and geometric inequalities for convex bodies

Abstract

All Science Journal Classification (ASJC) codes

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