Eigenvalues and Minimal Surfaces
Offered By: Centre de recherches mathématiques - CRM via YouTube
Course Description
Overview
Explore the fascinating world of eigenvalues and minimal surfaces in this illuminating lecture by Mikhail Karpukhin from University College London. Delve into the intriguing connection between Laplace operator eigenvalues and physical phenomena such as heat flow and sound propagation. Trace the history of eigenvalue inequalities from Lord Rayleigh's 19th-century question about the lowest first Dirichlet eigenvalue in planar domains to modern isoperimetric problems involving Riemannian metrics on surfaces. Discover recent advancements in sharp upper bounds for Laplace and Steklov eigenvalues, and their profound link to minimal surface theory. Gain insights into the applications of this connection in both minimal surface theory and isoperimetric eigenvalue problems, culminating in an unexpected relationship between Laplace and Steklov spectra.
Syllabus
Mikhail Karpukhin: Eigenvalues and minimal surfaces
Taught by
Centre de recherches mathématiques - CRM
Related Courses
On Yuansi Chen's Work on the KLS Conjecture IIIHausdorff Center for Mathematics via YouTube On Yuansi Chen's Work on the KLS Conjecture I
Hausdorff Center for Mathematics via YouTube Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2
ICTP Mathematics via YouTube On Yuansi Chen's Work on the KLS Conjecture II
Hausdorff Center for Mathematics via YouTube Isoperimetric Problem- From Classical to Reverse I
Hausdorff Center for Mathematics via YouTube