Maximal volume entropy rigidity for RCD∗(−(N−1),N) spaces
Chris Connell, Xianzhe Dai, Jesús Núñez‐Zimbrón, Raquel Perales, Pablo Suárez–Serrato, Guofang Wei
Abstract
For n-dimensional Riemannian manifolds M with Ricci curvature bounded below by − ( n − 1 ) , the volume entropy is bounded above by n − 1 . If M is compact, it is known that the equality holds if and only if M is hyperbolic. We extend this result to RCD ∗ ( − ( N − 1 ) , N ) spaces. While the upper bound is straightforward, the rigidity case is quite involved due to the lack of a smooth structure in RCD ∗ spaces. As an application, we obtain an almost rigidity result which partially recovers a result by Chen–Rong–Xu for Riemannian manifolds.
Topics & Concepts
Rigidity (electromagnetism)MathematicsStatistical physicsPhysicsQuantum mechanicsGeometric Analysis and Curvature FlowsGeometry and complex manifoldsNonlinear Partial Differential Equations