Existence and Uniqueness for the Non-Compact Yamabe Problem of Negative Curvature Type  

作　　者：Joseph Hogg Luc Nguyen 

机构地区：[1]Mathematical Institute and St Edmund Hall,University of Oxford,Andrew Wiles Building,Radcliffe Observatory Quarter,Woodstock Road,Oxford OX26GG,UK

出　　处：《Analysis in Theory and Applications》2024年第1期57-91,共35页分析理论与应用（英文刊）

基　　金：supported by the EPSRC Centre for Doctoral Training in Partial Differential Equations(grant number EP/L015811/1).

摘　　要：We study existence and uniqueness results for the Yamabe problem on non-compact manifolds of negative curvature type.Ourfirst existence and uniqueness result concerns those such manifolds which are asymptotically locally hyperbolic.In this context,our result requires only a partial C2 decay of the metric,namely the full decay of the metric in C1 and the decay of the scalar curvature.In particular,no decay of the Ricci curvature is assumed.In our second result we establish that a local volume ratio condition,when combined with negativity of the scalar curvature at infinity,is sufficient for existence of a solution.Our volume ratio condition appears tight.This paper is based on the DPhil thesis of thefirst author.

关 键 词：Yamabe problem non-compact manifolds negative curvature asymptotically locally hyperbolic asymptotically warped product relative volume comparison non-smooth conformal compactification 

分 类 号：O17[理学—数学]