CMSA Math Science Literature Lecture Series
Camillo De Lellis - Institute for Advanced Study
TITLE: Area-minimizing integral currents and their regularity
ABSTRACT: Caccioppoli sets and integral currents (their generalization in higher codimension) were introduced in the late fifties and early sixties to give a general geometric approach to the existence of area-minimizing oriented surfaces spanning a given contour. These concepts started a whole new subject which has had tremendous impacts in several areas of mathematics: superficially through direct applications of the main theorems, but more deeply because of the techniques which have been invented to deal with related analytical and geometrical challenges. In this lecture I will review the basic concepts, the related existence theory of solutions of the Plateau problem, and what is known about their regularity. I will also touch upon several fundamental open problems which still defy our understanding.
Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”
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