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

YouTube

Area-Minimizing Integral Currents: Singularities and Structure - Lecture

Institut des Hautes Etudes Scientifiques (IHES) via YouTube

Overview

Explore the intricacies of area-minimizing integral currents in this advanced mathematics lecture. Delve into the generalization of area-minimizing oriented surfaces, pioneered by De Giorgi and extended by Federer and Fleming. Examine celebrated examples of singular minimizers and dimension bounds for singular sets in various codimensions. Investigate recent developments, including Liu's result on fractal singular sets and progress towards proving the conjecture of $(m-2)$-rectifiability. Learn about oriented Plateau problems, integral currents, rectifiability, and key theorems in the field. Gain insights into monotonicity formulas and Federal reduction arguments as Camillo de Lellis from the Institute for Advanced Study presents recent joint works with Anna Skorobogatova and Paul Minter.

Syllabus

Introduction
Oriented Plateau Problem
Integral Currents
Integral Rectifiable
Fundamental Theorem
Regularity Theorem
Minimizers Theorem
Main Theorem
Monotonicity Formula
Federal Reduction Argument

Taught by

Institut des Hautes Etudes Scientifiques (IHES)

Reviews

Start your review of Area-Minimizing Integral Currents: Singularities and Structure - Lecture

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.