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.
Copyright © 2019 Springer US. Article first published online: September 2018.
The definitive version is available at: https://link.springer.com/article/10.1007%2Fs12220-018-0093-4
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Benson, Brian, Ivan Blank, and Jeremy LeCrone. "Mean Value Theorems for Riemannian Manifolds via the Obstacle Problem." The Journal of Geometric Analysis 29, no. 3 (July 2019): 2752-2775. https://doi.org/ 10.1007/s12220-018-0093-4.
Benson, Brian; Blank, Ivan; and LeCrone, Jeremy, "Mean Value Theorems for Riemannian Manifolds Via the Obstacle Problem" (2019). Math and Computer Science Faculty Publications. 218.