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arXiv · 1309.4664

On the Bakry-\'Emery condition, the gradient estimates and the Local-to-Global property of RCD*(K,N) metric measure spaces

Luigi Ambrosio·Andrea Mondino·Giuseppe Savaré
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Abstract

We prove higher summability and regularity of \Gamma(f) for functions f in spaces satisfying the Bakry-\'Emery condition BE(K,\infty). As a byproduct, we obtain various equivalent weak formulations of BE(K,N) and we prove the Local-to-Global property of the RCD*(K,N) condition in locally compact metric measure spaces (X,d,m), without assuming a priori the non-branching condition on the metric space.

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Luigi Ambrosio, Andrea Mondino, Giuseppe Savaré. 2013-09-18. On the Bakry-\'Emery condition, the gradient estimates and the Local-to-Global property of RCD*(K,N) metric measure spaces. https://doi.org/10.1007/s12220-014-9537-7.

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