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We prove results relating the theory of optimal transport and generalized Ricci flow. We define an adapted cost functional for measures using a solution of the associated dilaton flow. This determines a formal notion of geodesics in the space of measures, and we show geodesic convexity of an associated entropy functional. Finally, we show monotonicity of the cost along the backwards heat flow, and use this to give a new proof of the monotonicity of the energy functional along generalized Ricci flow.
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Ricci flow on Courant algebroids
We develop a theory of Ricci flow for metrics on Courant algebroids which unifies and extends the analytic theory of various geometric flows, yielding a general tool for constructing solutions to supergravity equations. We prove short-time existence and uniqueness of solutions on compact manifolds, in turn showing that the Courant isometry group is preserved by the flow. We show a scalar curvature monotonicity formula and prove that generalized Ricci flow is a gradient flow, extending fundamental works of Hamilton and Perelman. Using these we show a convergence result for certain nonsingular solutions to generalized Ricci flow.
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- Award ID(s):
- 2203536
- PAR ID:
- 10625364
- Publisher / Repository:
- World Scientific
- Date Published:
- Journal Name:
- Communications in Contemporary Mathematics
- ISSN:
- 0219-1997
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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