2023/07/11 by Kingshook Biswas, Biswas, Kingshook, Utsav Dewan +1
Computer Science · Mathematics · #31C12 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2307.05215
openalex publication_date 2023/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A well studied classical problem is the harmonicity of functions satisfying the restricted mean-value property (RMVP). While this has so far been studied mainly for domains in ℝn, we consider this problem in the general setting of domains in Riemannian manifolds, and obtain results generalizing classical results of Fenton. We also obtain a result for complete, simply connected Riemannian manifolds of pinched negative curvature where there is no restriction on the radius function in the RMVP.