Spherical Plateau Problem and Applications in Geometric Analysis
Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Course Description
Overview
Explore a lecture on the Spherical Plateau problem and its applications, delivered by Antoine Song from Caltech at the Institut des Hautes Etudes Scientifiques (IHES). Delve into an area minimization problem in certain quotients of the Hilbert sphere by countable groups, examining its origins in Besson-Courtois-Gallot's work on entropy inequality. Discover stability results derived from this minimization problem, including an analysis of closed surfaces of genus at least 2 with Riemannian metrics. Learn about the relationship between volume entropy, first eigenvalue, and hyperbolic metrics, and understand the stability of the hyperbolic plane in Benjamini-Schramm topology. Follow the lecture's outline, covering topics such as Gamma-compactness theorem, geometrization, hyperbolic manifolds, volumetropy inequality, and convergence over the course of one hour.
Syllabus
Outline
Problem
Gamma
Compactness Theorem
Motivation
Questions
Geometricization
Hyperbolic manifolds
Open questions
Volumetropy
Inequality
Statement
Topology
Convergence
Taught by
Institut des Hautes Etudes Scientifiques (IHES)
Related Courses
Nonlinear Dynamics 1: Geometry of ChaosGeorgia Institute of Technology via Independent Geometría diferencial y Mecánica: una introducción
Universidad de La Laguna via Miríadax Geometría diferencial y Mecánica: una introducción
Universidad de La Laguna via Miríadax Differential Geometry
Math at Andrews via YouTube On Gradient-Based Optimization - Accelerated, Distributed, Asynchronous and Stochastic
Simons Institute via YouTube