On the isometry group of $RCD^*(K,N)$-spaces

Luis Guijarro; Jaime Santos-Rodríguez

On the isometry group of $RCD^*(K,N)$-spaces

Differential Geometry 2018-07-26 v2 Metric Geometry

Authors: Luis Guijarro , Jaime Santos-Rodríguez

Abstract

We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $RCD^*(K,N),$ 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.

Keywords

RCD*(K,N) spaces isometry group Lie group metric measure space Riemannian curvature condition dimension bound

Cite

@article{arxiv.1608.06467,
  title  = {On the isometry group of $RCD^*(K,N)$-spaces},
  author = {Luis Guijarro and Jaime Santos-Rodríguez},
  journal= {arXiv preprint arXiv:1608.06467},
  year   = {2018}
}

Comments

Several proofs have been simplified

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