Spring 2027
Natasa Sesum
Subtitle:
Mean curvature flow
Course Description:
We will introduce mean curvature flow equation. We will introduce basic tools used in study of MCF equation, such as the maximum principle and integral estimates. In the first part of the class we will talk about smooth solutions, Huisken's monotonicity formula, self-similar solutions of the MCF and other possible singularity models, classification of all possible singularities in the case the flow is mean convex. We will also talk about the regularity theory at the first singular time, including the White's local regularity gap theorem and Brakke's estimate on the size of the singular set.In the second part of the class we will introduce the notion of weak Brakke solutions to the MCF in the measure theoretic sense. We will talk about the compactness theorem for integral Brakke flows, elliptic regularization, and the level set flow.
Textbook:
Klaus Ecker: Regularity theory for MCF
Prerequisites:
partial differential equations
Schedule of Sections:
16:640:510 Schedule of Classes
Previous Semesters
- Spring 2025 - Sesum, Natasa
- Fall 2023 - Xu, Guangbo
- Spring 2023 - Sesum, Natasa
- Spring 2022 - Mirek, Mariusz
- Fall 2020 Prof. A. Soffer
- Fall 2019 Prof. Brezis