Brownian Motions and Heat Kernel Lower Bounds on Kähler and Quaternion Kähler Manifolds

Fabrice Baudoin; Guang Yang

doi:10.1093/imrn/rnaa199

Brownian Motions and Heat Kernel Lower Bounds on Kähler and Quaternion Kähler Manifolds

^*Corresponding author for this work

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5 Citations (Scopus)

Abstract

We study the radial parts of the Brownian motions on Kähler and quaternion Kähler manifolds. Thanks to sharp Laplacian comparison theorems, we deduce as a consequence a sharp Cheeger-Yau-type lower bound for the heat kernels of such manifolds and also sharp Cheng's type estimates for the Dirichlet eigenvalues of metric balls.

Original language	English
Journal	International Mathematics Research Notices
Volume	2022
Issue	6
Pages (from-to)	4659-4681
Number of pages	23
ISSN	1073-7928
DOIs	https://doi.org/10.1093/imrn/rnaa199
Publication status	Published - 1 Mar 2022
Externally published	Yes

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10.1093/imrn/rnaa199

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title = "Brownian Motions and Heat Kernel Lower Bounds on K{\"a}hler and Quaternion K{\"a}hler Manifolds",

abstract = "We study the radial parts of the Brownian motions on K{\"a}hler and quaternion K{\"a}hler manifolds. Thanks to sharp Laplacian comparison theorems, we deduce as a consequence a sharp Cheeger-Yau-type lower bound for the heat kernels of such manifolds and also sharp Cheng's type estimates for the Dirichlet eigenvalues of metric balls.",

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T1 - Brownian Motions and Heat Kernel Lower Bounds on Kähler and Quaternion Kähler Manifolds

AU - Baudoin, Fabrice

AU - Yang, Guang

PY - 2022/3/1

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N2 - We study the radial parts of the Brownian motions on Kähler and quaternion Kähler manifolds. Thanks to sharp Laplacian comparison theorems, we deduce as a consequence a sharp Cheeger-Yau-type lower bound for the heat kernels of such manifolds and also sharp Cheng's type estimates for the Dirichlet eigenvalues of metric balls.

AB - We study the radial parts of the Brownian motions on Kähler and quaternion Kähler manifolds. Thanks to sharp Laplacian comparison theorems, we deduce as a consequence a sharp Cheeger-Yau-type lower bound for the heat kernels of such manifolds and also sharp Cheng's type estimates for the Dirichlet eigenvalues of metric balls.

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U2 - 10.1093/imrn/rnaa199

DO - 10.1093/imrn/rnaa199

M3 - Journal article

AN - SCOPUS:85115012649

SN - 1073-7928

VL - 2022

SP - 4659

EP - 4681

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 6

ER -

Brownian Motions and Heat Kernel Lower Bounds on Kähler and Quaternion Kähler Manifolds

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