Diameter estimate for planar 𝐿_{𝑝} dual Minkowski problem

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-05-22 DOI:10.1090/proc/16464

Minhyun Kim, Taehun Lee

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引用次数: 0

Abstract

In this paper, given a prescribed measure on S 1 \mathbb {S}^1 whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar L p L_p dual Minkowski problem when 0 > p > 1 0>p>1 and q ≥ 2 q\ge 2 . We also prove the uniqueness and positivity of solutions to the L p L_p Minkowski problem when the density of the measure is sufficiently close to a constant in C α C^\alpha .

查看原文本刊更多论文

平面𝐿_{𝑝} 对偶闵科夫斯基问题的直径估计

在本文中，给定 S 1 \mathbb {S}^1 上密度有界且为正的规定度量，当 0 > p > 1 0>p>1 且 q≥ 2 q\ge 2 时，我们建立了平面 L p L_p 对偶闵科夫斯基问题解的均匀直径估计。我们还证明了当度量密度足够接近 C α C^\alpha 中的一个常数时，L p L_p Minkowski 问题解的唯一性和实在性。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.