Stochastic Ricci Flow on Compact Surfaces

Understand

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 &#34;$L^1$ regime&#34; $\sigma< \sigma_{L^1}=2\sqrt\pi$ where $\sigma$ is the noise strength.
• We also describe the main necessary modifications needed for the SRF on general compact surfaces, and list some open questions.