Restricted mean value property on Riemannian manifolds

Kingshook Biswas; Utsav Dewan

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arXiv · 2307.05215

Restricted mean value property on Riemannian manifolds

Kingshook Biswas·Utsav Dewan

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Abstract

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 $\mathbb{R}^n$, 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.

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Kingshook Biswas, Utsav Dewan. 2023-07-11. Restricted mean value property on Riemannian manifolds. https://arxiv.org/abs/2307.05215

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