On the Bakry–Émery Condition, the Gradient Estimates and the Local-to-Global Property of \(\mathsf{RCD}^*(K,N)\) Metric Measure Spaces
文摘
We prove higher summability and regularity of \(\Gamma \big (f\big )\) for functions \(f\) in spaces satisfying the Bakry–Émery condition \(\mathsf{BE}(K,\infty )\). As a byproduct, we obtain various equivalent weak formulations of \(\mathsf{BE}(K,N)\) and we prove the Local-to-Global property of the \(\mathsf{RCD}^*(K,N)\) condition in locally compact metric measure spaces \((X,\mathsf{d},\mathfrak m)\), without assuming a priori the non-branching condition on the metric space. Keywords Bakry–Émery curvature bounds Dirichlet forms CD (K, N) spaces Optimal transport