2017/06/01 by Seongtag Kim, Kim, Seongtag
Computer Science · Mathematics · #53C21 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1706.00460
openalex publication_date 2017/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (M, g) be an n-dimensional complete Riemannian manifold. In this paper, we considers the following conformal scalar curvature rigidity problem: Given a compact smooth domain Ω with ∂ Ω, can one find a conformal metric g whose scalar curvature R[g]≥ R[ g] on Ω and the mean curvature H[g] ≥ H[ g] on ∂ Ω with g = g on ∂ Ω? We prove that g = g on some smooth domains in a general Riemannian manifold, which is an extension of the previous results given by Qing and Yuan, and Hang and Wang.