We prove the scalar curvature rigidity for L infinity metrics on S'\Sigma, where S' is the n-dimensional sphere with n >= 3 and Sigma is a closed subset of S' of codimension at least '2 + 1 that satisfies the wrapping property. The notion of wrapping property was introduced by the second author for studying related scalar curvature rigidity problems on spheres. For example, any closed subset of S' contained in a hemisphere and any finite subset of S' satisfy the wrapping property. The same techniques also apply to prove an analogous scalar rigidity result for L infinity metrics on tori that are smooth away from certain subsets of codimension at least '2 + 1. As a corollary, we obtain a positive mass theorem for complete asymptotically flat spin manifolds with arbitrary ends for L infinity metrics. (c) 2026 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

Publication:

ADVANCES IN MATHEMATICS

http://dx.doi.org/10.1016/j.aim.2026.111039

Author:

Wang, Jinmin

Chinese Acad Sci, Inst Math, Beijing, Peoples R China

Email address: jinmin@amss.ac.cn

Xie, Zhizhang (corresponding author)

Texas ABM Univ, Dept Math, College Stn, TX 77843 USA

Email address: xie@tamu.edu