Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA

Institute for Pure & Applied Mathematics (IPAM) via YouTube

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore a 24-minute lecture on "Entropy and C^0 stability of hypersurfaces" presented by Jacob Bernstein from Johns Hopkins University at IPAM's Calculus of Variations in Probability and Geometry Workshop. Delve into Colding and Minicozzi's concept of entropy as a measure of submanifold complexity in Euclidean space, and examine how round spheres uniquely minimize this entropy for closed hypersurfaces. Investigate the stability of this rigidity property, focusing on Lu Wang and Bernstein's perspective that demonstrates how closed surfaces in R^3 with entropy close to that of the round two-sphere are similar as closed sets. Discover various generalizations and related questions in this field, covering topics such as sharp inequality, basic properties, nonclosed singularity, quantitative versions, higher dimensions, and thinness.

Syllabus

Intro
Sharp inequality
Stability as a set
Basic properties
Nonclosed singularity
Bonus
Proof
Quantitative version
Higher dimensions
Thinness

Taught by

Institute for Pure & Applied Mathematics (IPAM)

Reviews

Start your review of Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.