Stochastic Ricci Flow on Compact Surfaces

  title={Stochastic Ricci Flow on Compact Surfaces},
  author={Julien Dub'edat and Hao Shen},
  journal={arXiv: Probability},
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… 
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  • G. Remy
  • Mathematics
    Journal of Mathematical Physics
  • 2018
In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists