On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow

doi:10.1515/agms-2022-0152

淡江大學機構典藏 > 理學院 > 應用數學與數據科學學系 > 期刊論文 > Item 987654321/124456

jsp.display-item.identifier=請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/124456

题名:	On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow
作者:	Ho, Pak-tung
关键词:	Yamabe problem;Yamabe soliton;smooth metric measure space
日期:	2023-04-28
上传时间:	2023-09-07 12:05:30 (UTC+8)
出版者:	De Gruyter
摘要:	The weighted Yamabe problem introduced by Case is the generalization of the Gagliardo-Nirenberg inequalities to smooth metric measure spaces. More precisely, given a smooth metric measure space (M,g,e−ϕdVg,m) , the weighted Yamabe problem consists on finding another smooth metric measure space conformal to (M,g,e−ϕdVg,m) such that its weighted scalar curvature is equal to λ+μe−ϕ∕m for some constants μ and λ , satisfying a certain condition. In this article, we consider the problem of prescribing the weighted scalar curvature. We first prove some uniqueness and nonuniqueness results and then some existence result about prescribing the weighted scalar curvature. We also estimate the first nonzero eigenvalue of the weighted Laplacian of (M,g,e−ϕdVg,m) . On the other hand, we prove a version of the conformal Schwarz lemma on (M,g,e−ϕdVg,m) . All these results are achieved by using geometric flows related to the weighted Yamabe flow. We also prove the backward uniqueness of the weighted Yamabe flow. Finally, we consider weighted Yamabe solitons, which are the self-similar solutions of the weighted Yamabe flow.
關聯:	Analysis and Geometry in Metric Spaces 11(1),　20220152
DOI:	10.1515/agms-2022-0152
显示于类别:	[應用數學與數據科學學系] 期刊論文

文件中的档案:

档案	描述	大小	格式	浏览次数
index.html		0Kb	HTML	94	检视/开启

在機構典藏中所有的数据项都受到原著作权保护.

TAIR相关文章

数据加载中.....