On the isometry group of $RC{D}^{\ast }(K,N)$-spaces

Abstract

We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $RC{D}^{\ast }(K,N),$ is in fact a Lie group. We obtain an optimal upper bound on its dimension and classify the spaces where this maximal dimension is achieved.

Several proofs have been simplified

References in corpus (3)

• Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts
• Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces
• The isometry group of an ${\mathsf{RCD}}^{\ast }$-space is Lie

Cited by in corpus (2)

• On quotients of spaces with Ricci curvature bounded below
• The isometry group of an ${\mathsf{RCD}}^{\ast }$-space is Lie