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Title: Stochastic Ricci Flow on Compact Surfaces
Abstract 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 surfaces and list some open questions.  more » « less
Award ID(s):
1954091
NSF-PAR ID:
10326369
Author(s) / Creator(s):
;
Date Published:
Journal Name:
International Mathematics Research Notices
ISSN:
1073-7928
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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