Stochastic Ricci Flow on Compact Surfaces

Wed, 24 Apr 2019 00:00:00 GMT

Julien Dubédat, Hao Shen — 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 "L¹ regime" σ< σ_(L¹)=2sqrtπ where σ is the noise strength. We also describe the main necessary modifications needed for the SRF on general compact surfaces, and list some open questions.

Julien Dubédat — Neckpinch

Stochastic Ricci Flow on Compact Surfaces