# Improved regularity estimates for Lagrangian flows on $\text{RCD}(K,N)$ spaces

@inproceedings{Bru2021ImprovedRE, title={Improved regularity estimates for Lagrangian flows on \$\text\{RCD\}(K,N)\$ spaces}, author={Elia Bru{\'e} and Qintao Deng and Daniele Semola}, year={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 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…

## One Citation

### Parallel transport on non-collapsed $\mathsf{RCD}(K,N)$ spaces

- Mathematics
- 2021

We provide a general theory for parallel transport on non-collapsed ${\sf RCD}$ spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and, more generally, of…

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