Cheeger-harmonic functions in metric measure spaces revisited

Renjin Jiang

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arXiv · 1307.1334

Cheeger-harmonic functions in metric measure spaces revisited

Renjin Jiang

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Abstract

Let $(X,d,μ)$ be a complete metric measure space, with $μ$ a locally doubling measure, that supports a local weak $L^2$-Poincaré inequality. By assuming a heat semigroup type curvature condition, we prove that Cheeger-harmonic functions are Lipschitz continuous on $(X,d,μ)$. Gradient estimates for Cheeger-harmonic functions and solutions to a class of non-linear Poisson type equations are presented.

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Renjin Jiang. 2013-07-14. Cheeger-harmonic functions in metric measure spaces revisited. https://arxiv.org/abs/1307.1334

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