Minicourse on "Mean curvature flow and related topics"
By Francisco Martín (U. Granada)
We recommend the pre-course on
The aim of these lectures is giving a brief idea about singularity formation, non-uniqueness and topological change under motion by mean curvature. Mean curvature flow arises as a simplified model in several physical problems where surface tension plays a role.
- Mean curvature flows in Euclidean space.
- 1.1 Introduction.
- 1.2 Existence.
- 1.3 Geometric evolution equations.
- 1.4 Comparison principle.
- 1.5 Examples.
- Singularities and solitons.
- 2.1 Types of singularities.
- 2.2 Integral estimates and monotonicity formulas.
- 2.3 Solitons.
-Ecker, K.: Regularity Theory for Mean Curvature Flow. Birkhäuser (2004).
-Mantegazza, C: Lecture Notes on Mean Curvature Flow. Birkhäuser (2011).
-Martín F. and Pérez J.: Lecture notes on Mean curvature flow and related topics (2014). To be delivered at the meeting.
-Ritoré M. and Sinestrari C.: Mean Curvature Flow and Isoperimetric Inequalities. Birkhäuser (2010).
-Smoczyk, K.: Mean Curvature Flow in higher codimension. Introduction and survey. Preprint, arXiv:1104.3222 [math.DG].