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

By Luigi Ambrosio, Andrea Mondino, Giuseppe Savar'e. 2013

126 citations recorded by the source corpus.

We prove higher summability and regularity of (cid:2) (cid:2) f (cid:3) for functions f in spaces satisfying the Bakry–Émery condition BE ( K , ∞ ) . 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

View Paper: https://www.semanticscholar.org/paper/c2f6da1991bcbaf41c19ef0518ec54d896627694

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Citations in the corpus

• The globalization theorem for the Curvature-Dimension condition (2016, background): “Let us also mention here the work of Ambrosio–Mondino–Savaré [10], who independently of a similar result in [35], established the local-to-global property for RCD∗(K,N) proper spaces, K ∈ R and N ∈ [1,∞], without a-priori assuming any non-branching assumptions (but a-posteriori, such spaces must be”