The $L_p$ Gauss image problem

Chuanxi Wu; Di Wu; Ni Xiang

arXiv:2105.02463·math.AP·May 7, 2021

The $L_p$ Gauss image problem

Chuanxi Wu, Di Wu, Ni Xiang

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TL;DR

This paper investigates the $L_p$ Gauss image problem, a generalization of classical convex geometry problems, providing existence results for certain parameter ranges and measure conditions.

Contribution

It establishes the existence of solutions for the $L_p$ Gauss image problem in cases where p is positive or negative with even measures.

Findings

01

Existence results for $p>0$

02

Existence results for $p<0$ with even measures

03

Generalization of classical convex geometry problems

Abstract

In this paper we study the $L_{p}$ Gauss image problem, which is a generalization of the $L_{p}$ Aleksandrov problem and the Gauss image problem in convex geometry. We obtain the existence result for the $L_{p}$ Gauss image problem in two cases (i) $p > 0$ or (ii) $p < 0$ with the given even measures.

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