Yoshihiro Tonegawa's Intro to Brakke's Mean Curvature Flow | Interface Evolution Series

The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces. Abstract: Among numerous evolution problems involving interface, the mean curvature flow stands out for its simplicity, depth, and width of relevant subfields. The aim of this mini-course is to acquaint the audience with the notion of mean curvature flow in the setting of Geometric Measure Theory called the Brakke flow. Followed by a quick review of the necessary preliminary materials from Geometric Measure Theory, I will explain the definition of Brakke flow and describe the basic properties such as Huisken’s monotonicity formula, the compactness theorem and the existence of tangent flows. In the remaining time, I will discuss the epsilon regularity theorem which is the parabolic analogue of the Allard regularity theorem.