Kähler和Kähler四元数流形上的布朗运动和热核下界

arXiv: Differential Geometry Pub Date : 2020-03-12 DOI:10.1093/imrn/rnaa199

Fabrice Baudoin, Guang Yang

{"title":"Kähler和Kähler四元数流形上的布朗运动和热核下界","authors":"Fabrice Baudoin, Guang Yang","doi":"10.1093/imrn/rnaa199","DOIUrl":null,"url":null,"abstract":"We study the radial parts of the Brownian motions on K\\\"ahler and quaternion K\\\"ahler 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.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Brownian Motions and Heat Kernel Lower Bounds on Kähler and Quaternion Kähler Manifolds\",\"authors\":\"Fabrice Baudoin, Guang Yang\",\"doi\":\"10.1093/imrn/rnaa199\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the radial parts of the Brownian motions on K\\\\\\\"ahler and quaternion K\\\\\\\"ahler 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.\",\"PeriodicalId\":8430,\"journal\":{\"name\":\"arXiv: Differential Geometry\",\"volume\":\"26 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnaa199\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/imrn/rnaa199","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 8

摘要

研究了K\ ahler流形和四元数K\ ahler流形上布朗运动的径向部分。借助于尖锐的拉普拉斯比较定理，我们推导出了这种流形的热核的尖锐Cheeger-Yau型下界和度量球的Dirichlet特征值的尖锐Cheng型估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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

We study the radial parts of the Brownian motions on K\"ahler and quaternion K\"ahler 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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: Differential Geometry

自引率

0.00%

发文量