Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces
2021
This paper gives a contribution to the study of regularity of Lagrangian flows on
non-smooth spaces with lower Ricci curvature bounds. The main novelties with respect to the
existing literature are the better behaviour with respect to time and the local nature of the
regularity estimates. These are obtained by sharpening previous results of the first and third
authors, in combination with some tools recently developed by the second author (adapting to
the synthetic framework ideas introduced in [CoN12]).
The estimates are suitable for applications to the fine study of RCD spaces and play a central
role in the construction of a parallel transport in this setting.
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