Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems
Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems
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非线性 Yamabe 问题格林函数的存在性与唯一性
DOI：
10.1002/cpa.22044
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发表时间：
2020-01
影响因子：
3
通讯作者：
Yanyan Li;Luc Nguyen
中科院分区：
文献类型：
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作者：
Yanyan Li;Luc Nguyen
对于紧致黎曼流形(M，g)的一个给定的有限子集S，其Schouten曲率张量属于给定的锥，我们建立了M\S上存在唯一共形度量的充要条件，使得S的每个点对应于渐近平坦的一端，且该共形度量的Schouten张量属于给定锥的边界.作为副产品，我们定义了与光滑度量共形的连续度量的Ricci下界的纯局部概念，并证明了相应的体积比较定理。©2022作者。《纯粹数学与应用数学通讯》由威利期刊有限责任公司出版。
For a given finite subset S of a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M\S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the conformal metric belongs to the boundary of the given cone. As a by‐product, we define a purely local notion of Ricci lower bounds for continuous metrics that are conformal to smooth metrics and prove a corresponding volume comparison theorem. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.