Stochastic Ricci Flow on Compact Surfaces-Reference-Cited by-同舟云学术

Stochastic Ricci Flow on Compact Surfaces

Published:2021-04-19 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Dubédat Julien¹,Shen Hao²

Affiliation:

1. Columbia University, Department of Mathematics, New York 10027, USA

2. University of Wisconsin-Madison, Department of Mathematics, Madison 53706, USA

Abstract

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.

Funder

National Science Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab015/37112534/rnab015.pdf

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