p$谐函数的单调量及其应用

IF 0.5 4区数学 Q3 MATHEMATICS

Pure and Applied Mathematics Quarterly Pub Date : 2024-04-03 DOI:10.4310/pamq.2024.v20.n2.a1

Sven Hirsch, Pengzi Miao, Luen-Fai Tam

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引用次数: 0

摘要

我们推导了具有非负标量曲率的流形上与 $p$ 谐函数相关的局部和全局单调量。作为应用，我们得到了与渐近平坦的$3$流形的质量、$p$容量和边界的威尔摩尔函数相关的不等式。当 $p \to 1$ 时，其中一个结果检索到一个经典关系，即如果曲面是面积外最小的，则 ADM 质量支配霍金质量。

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Monotone quantities of $p$-harmonic functions and their applications

We derive local and global monotonic quantities associated to $p$-harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the $p$-capacity and the Willmore functional of the boundary. As $p \to 1$, one of the results retrieves a classic relation that the ADM mass dominates the Hawking mass if the surface is area outer-minimizing.

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来源期刊

Pure and Applied Mathematics Quarterly 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality, original papers on all fields of mathematics. To facilitate fruitful interchanges between mathematicians from different regions and specialties, and to effectively disseminate new breakthroughs in mathematics, the journal welcomes well-written submissions from all significant areas of mathematics. The editors are committed to promoting the highest quality of mathematical scholarship.