Fully nonlinear flows with surgery
Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016
Location: MSRI: Simons Auditorium
singularities of flows
surgery on flows
53C56 - Other complex differential geometry [See also 32Cxx]
53C44 - Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
53Cxx - Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]
53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20]
53C45 - Global surface theory (convex surfaces à la A. D. Aleksandrov)
We will present joint work with Gerhard Huisken on a fully nonlinear flow for hypersurfaces in Riemannian manifolds. Unlike mean curvature flow, this flow preserves two-convexity in a general ambient manifold. For this fully nonlinear flow, we establish a convexity estimate, a cylindrical estimate, and a pointwise curvature derivative estimate. These estimates allow us to extend the flow beyond singularities by a surgery procedure, similar to the ones developed by Hamilton and Perelman for the Ricci flow and by Huisken and Sinestrari for mean curvature flow
Please report video problems to email@example.com.
See more of our Streaming videos on our main VMath Videos page.