Harmonic Functions on Metric Measure Spaces: Convergence and Compactness

Gaczkowski M; Gorka P

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Harmonic Functions on Metric Measure Spaces: Convergence and Compactness

机译：度量度量空间上的调和函数：收敛性和紧致性

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摘要

We investigate the properties of harmonic functions defined on a metric measure space. Especially, sequences of harmonic functions are examined, i.e. their convergence and compactness. Moreover, Harnack's inequality is shown.

机译：我们研究在度量度量空间上定义的谐波函数的性质。特别地，检查谐波函数的序列，即它们的收敛性和紧凑性。此外，还显示了哈纳克不等式。

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来源
《Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis》 |2009年第3期|共12页
作者
Gaczkowski M; Gorka P;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Metric measure spaces; Continuous measure; Harmonic functions; Montel; theorem; Compactness;

机译：度量度量空间;连续度量;调和函数;Montel;定理;紧性;

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专利

1. Harmonic Functions on Metric Measure Spaces: Convergence and Compactness [J] . Michał Gaczkowski, Przemysław Górka Potential Analysis . 2009,第3期

机译：度量度量空间上的调和函数：收敛性和紧致性
2. Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows [J] . Gigli Nicola, Mondino Andrea, Savare Giuseppe Proceedings of the London Mathematical Society . 2015,第Pta5期

机译：尖的非紧致度量空间的收敛性以及Ricci曲率边界和热流的稳定性
3. Weighted p-harmonic functions and rigidity of smooth metric measure spaces [J] . Nguyen Thac Dung, Nguyen Duy Dat Journal of Mathematical Analysis and Applications . 2016,第2期

机译：加权p调和函数和光滑度量度量空间的刚度
4. Complexity Theory of (Functions on) Compact Metric Spaces [C] . Akitoshi Kawamura, Florian Steinberg, Martin Ziegler Annual ACM/IEEE Symposium on Logic in Computer Science . 2016

机译：紧度量空间的（复杂度）理论
5. Harmonic maps into metric spaces with curvature bounded above. [D] . Serbinowski, Tomasz. 1995

机译：调和映射到曲率在上面限定的度量空间中。
6. Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds [O] . Abhishek Bhattacharya, David B. Dunson -1

机译：具有特定歧管的紧凑型度量空间上的非参数贝叶斯密度估计的强稠度
7. Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows [O] . Gigli Nicola, Mondino Andrea, Savaré Giuseppe 2015

机译：尖的非紧致度量空间的收敛性以及Ricci曲率边界和热流的稳定性

Harmonic Functions on Metric Measure Spaces: Convergence and Compactness

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