Topological Properties of Hypersurfaces with Low Entropy - IPAM at UCLA

Explore a conference talk on the topological properties of hypersurfaces with low entropy, presented by Lu Wang of Yale University at IPAM's Calculus of Variations in Probability and Geometry Workshop. Delve into the concept of entropy for hypersurfaces, as defined by Colding and Minicozzi, which involves the supremum over Gaussian integrals with varying centers and scales. Discover recent findings on the topological characteristics of low-entropy hypersurfaces, a collaborative effort with Jacob Bernstein. Examine key topics including Colding-Minicozzi Entropy, Mean Curvature Flow, basic properties of entropy, entropy of planar curves and closed hypersurfaces, topological stability of round spheres, and the proof strategy for three-dimensional cases. Gain insights into this advanced mathematical concept and its implications in the field of geometry and topology.

Intro
Colding-Minicozzi Entropy
Mean Curvature Flow
Basic Properties of Entropy
Entropy of Planar Curves
Entropy of Closed Hypersurfaces
Topological Stability of Round Sphere
Strategy for the Proof in Dimension 3