Fully nonlinear flows with surgery
Geometric Flows in Riemannian and Complex Geometry May 02, 2016 - May 06, 2016
Location: SLMath: Eisenbud Auditorium
complex geometry
Riemannian geometry
geometric analysis
geometric flow
positive curvature
curvature flow
Ricci flow
singularities of flows
surgery on flows
hypersurfaces
Convex geometry
51D25 - Lattices of subspaces and geometric closure systems [See also 05B35]
51D30 - Continuous geometries, geometric closure systems and related topics [See also 06Cxx]
51A25 - Algebraization in linear incidence geometry [See also 12Kxx, 20N05]
14494
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
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