Mean Value Theorems for Riemannian Manifolds Via the Obstacle Problem

We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.

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Bibliographic Details
Published in:The Journal of geometric analysis 2019-07, Vol.29 (3), p.2752-2775
Main Authors: Benson, Brian, Blank, Ivan, LeCrone, Jeremy
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential calculus
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Riemann manifold
Theorems
Topological manifolds
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Description
Summary:We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-018-0093-4