A probabilistic approach to the maximal diameter theorem

Kazumasa Kuwada

doi:10.1002/mana.201100330

A probabilistic approach to the maximal diameter theorem

Kazumasa Kuwada

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Under a positive curvature and a finite dimension in terms of the Bakry-Émery tensor on a Riemannian manifold, the Bonnet-Myers type diameter bound and the rigidity theorem are extended. The corresponding second order generator need not be symmetrizable. The proof is based on the Laplacian comparison theorem and stochastic analysis of radial processes.

Original language	English
Pages (from-to)	374-378
Number of pages	5
Journal	Mathematische Nachrichten
Volume	286
Issue number	4
DOIs	https://doi.org/10.1002/mana.201100330
Publication status	Published - 2013 Mar
Externally published	Yes

Keywords

Bakry-Émery Ricci tensor
Bonnet-Myers theorem
Diffusion process
Laplacian comparison theorem
Maximal diameter theorem

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.201100330

Cite this

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title = "A probabilistic approach to the maximal diameter theorem",

abstract = "Under a positive curvature and a finite dimension in terms of the Bakry-{\'E}mery tensor on a Riemannian manifold, the Bonnet-Myers type diameter bound and the rigidity theorem are extended. The corresponding second order generator need not be symmetrizable. The proof is based on the Laplacian comparison theorem and stochastic analysis of radial processes.",

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author = "Kazumasa Kuwada",

year = "2013",

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AB - Under a positive curvature and a finite dimension in terms of the Bakry-Émery tensor on a Riemannian manifold, the Bonnet-Myers type diameter bound and the rigidity theorem are extended. The corresponding second order generator need not be symmetrizable. The proof is based on the Laplacian comparison theorem and stochastic analysis of radial processes.

KW - Bakry-Émery Ricci tensor

KW - Bonnet-Myers theorem

KW - Diffusion process

KW - Laplacian comparison theorem

KW - Maximal diameter theorem

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JF - Mathematische Nachrichten

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A probabilistic approach to the maximal diameter theorem

Abstract

Keywords

ASJC Scopus subject areas

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