Geometric Flows and PDE on Manifolds (ASUF - 30006602)

Project: Research project

Project Details

Description

Geometric Flows and PDE on Manifolds (ASUF - 30006602) Geometric flows and PDE on manifolds Since 2010, I have studied a number of problems for parabolic geometric evolution equations which all involve, in some way, an underlying question of uniqueness or unique continuation. My primary interest has been in the Ricci flow, however, I have recently begun to work on related problems for other equations, including the cross-curvature flow, the L2-curvature flow, and various other higher-order equations. The results I have obtained can be grouped into a few basic categories. Forward and backward uniqueness via energy/frequency methods. The analytic problems of forward and backward uniqueness for curvature flows such as the Ricci flow are closely linked (and often equivalent) to the fundamental geometric problem of whether the isometry group of a solution remains invariant under the flow. Curvature flows are not generally strictly parabolic, however, and the uniqueness of their solutions is not merely a consequence of standard parabolic theory.
StatusActive
Effective start/end date9/1/158/31/22

Funding

  • Simons Foundation: $35,000.00

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