# Stochastic Ricci Flow on Compact Surfaces

@article{Dubedat2019StochasticRF, title={Stochastic Ricci Flow on Compact Surfaces}, author={Julien Dub'edat and Hao Shen}, journal={arXiv: Probability}, year={2019} }

In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow is symmetric with respect to a measure induced by Liouville Conformal Field Theory. Using the theory of Dirichlet forms, we construct a weak solution to the associated equation of the area measure on a flat torus, in the full "$L^1$ regime" $\sigma< \sigma_{L^1}=2\sqrt\pi$ where $\sigma$ is the noise strength. We also describe the main necessary modifications needed for the SRF on general compact…

## 13 Citations

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