2024/01/04 by Xuezhang Chen, Chen, Xuezhang, Yalong Shi +1
Computer Science · Mathematics · #35J08 #53C24 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2401.02087
openalex publication_date 2024/01/04 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
We derive explicit representation formulae of Green functions for GJMS operators on n-spheres, including the fractional ones. These formulae have natural geometric interpretations concerning the extrinsic geometry of the round sphere. Conversely, we discover that this special feature uniquely characterizes spheres among closed embedded hypersurfaces in ℝn+1. Furthermore, for n=3,4,5 we prove a strong rigidity theorem for Green functions of hypersurfaces in ℝn+1 using the Positive Mass Theorem.