Bessel functions, heat kernel and the conical Kähler-Ricci flow

Xiuxiong Chen; Yuanqi Wang

doi:10.1016/j.jfa.2015.01.015

Bessel functions, heat kernel and the conical Kähler-Ricci flow

Xiuxiong Chen
, Yuanqi Wang

Mathematics

University of California at Santa Barbara
Simons Center for Geometry and Physics

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

31 Scopus citations

Abstract

Following Donaldson's openness theorem on deforming a conical Kähler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler-Ricci flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber formula on Bessel function of the second kind and Carslaw's heat kernel representation in [8].

Original language	English
Pages (from-to)	551-632
Number of pages	82
Journal	Journal of Functional Analysis
Volume	269
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2015.01.015
State	Published - Jul 15 2015

Keywords

Bessel functions
Heat kernel
Local existence conic Ricci flow
Schauder estimates

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10.1016/j.jfa.2015.01.015

Cite this

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title = "Bessel functions, heat kernel and the conical K{\"a}hler-Ricci flow",

abstract = "Following Donaldson's openness theorem on deforming a conical K{\"a}hler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical K{\"a}hler-Ricci flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber formula on Bessel function of the second kind and Carslaw's heat kernel representation in [8].",

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AU - Chen, Xiuxiong

AU - Wang, Yuanqi

PY - 2015/7/15

Y1 - 2015/7/15

N2 - Following Donaldson's openness theorem on deforming a conical Kähler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler-Ricci flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber formula on Bessel function of the second kind and Carslaw's heat kernel representation in [8].

AB - Following Donaldson's openness theorem on deforming a conical Kähler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical Kähler-Ricci flow exists for short time. The key is to establish the relevant heat kernel estimates, where we use the Weber formula on Bessel function of the second kind and Carslaw's heat kernel representation in [8].

KW - Bessel functions

KW - Heat kernel

KW - Local existence conic Ricci flow

KW - Schauder estimates

UR - https://www.scopus.com/pages/publications/84929706192

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DO - 10.1016/j.jfa.2015.01.015

M3 - Article

AN - SCOPUS:84929706192

SN - 0022-1236

VL - 269

SP - 551

EP - 632

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Bessel functions, heat kernel and the conical Kähler-Ricci flow

Abstract

Keywords

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