The L p chord Minkowski problem-Reference-Cited by-同舟云学术

The L _p chord Minkowski problem

Published:2023-01-01 Issue:1 Volume:23 Page:
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Xi Dongmeng¹²,Yang Deane²,Zhang Gaoyong²,Zhao Yiming³

Affiliation:

1. Department of Mathematics, Shanghai University , Shanghai 200444 , China

2. Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street , New York , NY 10012 , USA

3. Department of Mathematics, Syracuse University , Syracuse , NY 13244 , USA

Abstract

Abstract Chord measures are newly discovered translation-invariant geometric measures of convex bodies in

R n

{{\mathbb{R}}}^{n}

, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the

L p

{L}_{p}

chord measures is called the

L p

{L}_{p}

chord Minkowski problem in the

L p

{L}_{p}

Brunn-Minkowski theory, which includes the

L p

{L}_{p}

Minkowski problem as a special case. This article solves the

L p

{L}_{p}

chord Minkowski problem when

p > 1

p\gt 1

and the symmetric case of

0 < p < 1

0\lt p\lt 1

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2022-0041/pdf

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