Camillo DeLellis- Regular and Singular Minimal Surfaces
Explore the fascinating world of minimal surfaces in this lecture by Camillo DeLellis. Delve into the concept of surfaces whose area remains stationary under smooth perturbations, exemplified by area minimizers spanning given contours. Trace the historical roots of this field back to Lagrange's work in the 18th century. Examine the challenges posed by the non-smooth nature of these objects, questioning the very definitions of "surface" and "area." Investigate various mathematical approaches to generalized minimal surfaces, their distinctive features, and pivotal questions surrounding their smoothness, singularities, and behavior at singular points. Review classical works, recent advancements, and future challenges in this captivating area of mathematical research.