The Isometry Group of an RCD∗ Space is Lie

@article{Sosa2018TheIG,
  title={The Isometry Group of an RCD∗ Space is Lie},
  author={Gerardo Sosa},
  journal={Potential Analysis},
  year={2018},
  volume={49},
  pages={267-286}
}
We give necessary and sufficient conditions that show that both the group of isometries and the group of measure-preserving isometries are Lie groups for a large class of metric measure spaces. In addition we study, among other examples, whether spaces having a generalized lower Ricci curvature bound fulfill these requirements. The conditions are satisfied by RCD∗-spaces and, under extra assumptions, by CD-spaces, CD∗P-spaces. However, we show that the MCCP-condition by itself is not enough to… CONTINUE READING

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