On the Negativity of Ricci Curvatures of Complete Conformal Metrics  

作　　者：Qing Han Weiming Shen 

机构地区：[1]Department of Mathematics,University of Notre Dame,Notre Dame,IN 46556,USA [2]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Peking Mathematical Journal》2021年第1期83-117,共35页北京数学杂志（英文）

摘　　要：A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures.In this paper,we study whether these metrics have negative Ricci curvatures.Affirmatively,we prove that these metrics indeed have negative Ricci curvatures in bounded convex domains in the Euclidean space.On the other hand,we provide a general construction of domains in compact manifolds and demonstrate that the negativity of Ricci curvatures does not hold if the boundary is close to certain sets of low dimension.The expansion of the Green’s function and the positive mass theorem play essential roles in certain cases.

关 键 词：Negativity of Ricci curvatures The singular Yamabe problem Negative sectional curvatures 

分 类 号：O18[理学—数学]