$L_p$积分曲率的$L_p$-Alekandrov问题

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2018-09-01 DOI:10.4310/JDG/1536285625

Yong Huang, E. Lutwak, Deane Yang, Gaoyong Zhang

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引用次数: 47

摘要

结果表明，在Lp-Brunn–Minkowski理论中，Aleksandrov的积分曲率对所有实p都具有自然的Lp扩展。这就提出了在给定测度上寻找使其成为凸体的Lp积分曲率的充要条件的问题。这个问题对于正p是解决的，并且对于负p是回答的，前提是给定的测度是偶数。

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The $L_p$-Aleksandrov problem for $L_p$-integral curvature

It is shown that within the Lp-Brunn–Minkowski theory that Aleksandrov’s integral curvature has a natural Lp extension, for all real p. This raises the question of finding necessary and sufficient conditions on a given measure in order for it to be the Lp-integral curvature of a convex body. This problem is solved for positive p and is answered for negative p provided the given measure is even.

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来源期刊

Journal of Differential Geometry 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.