一般测度的Orlicz和Minkowski问题

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-01-09 DOI:10.1016/j.aam.2025.102839

Suwei Li, Qiuyue Chen, Hailin Jin

引用次数: 0

摘要

最近Lutwak-Xi-Yang-Zhang通过建立一组称为弦积分的基本积分几何不变量的变分公式，引入了弦测度和Lp弦测度。规定Lp弦测度称为Lp弦闵可夫斯基问题。Xi-Yang-Zhang-Zhao解决了Lp （p>1）弦Minkowski问题。本文研究了Orlicz弦Minkowski问题，将Lp（p>1）弦Minkowski问题推广为满足φ(0+)=∞和φ(∞)=0的定降连续函数φ:（0,∞）→（0,∞），并求解了离散测度和一般测度下的Orlicz弦Minkowski问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Orlicz chord Minkowski problem for general measures

Chord measures and

L_{p}

chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric invariants called chord integrals. Prescribing the

L_{p}

chord measures is called the

L_{p}

chord Minkowski problem. The

L_{p}

(

p > 1

) chord Minkowski problem was solved by Xi-Yang-Zhang-Zhao.

In the present paper, we investigate the Orlicz chord Minkowski problem, which generalizes the

L_{p} (p > 1)

chord Minkowski problem by replacing p with a fixed decreasing continuous function

φ : (0, \infty) \to (0, \infty)

satisfying

φ (0^{+}) = \infty

and

φ (\infty) = 0

, and solve the Orlicz chord Minkowski problem for discrete measures and the general measures.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.