Recent Developments in Constant Mean Curvature Hypersurfaces - Part I

Explore recent developments in constant mean curvature hypersurfaces through this 47-minute lecture by Xin Zhou from Cornell University. Delve into the existence theory of closed constant mean curvature hypersurfaces using the min-max method. Examine old and new open problems in this field, covering topics such as prescribed curvature, geometric measure theory, minimal hypersurfaces, and the first variation formula. Learn about the AC functional, min-max ideas, weak limits, and the almost minimizing concept. Investigate closed CMC surfaces, noncompact manifolds, and the Min-Max Theorem. Gain insights into multiplicity and the Area Functional as part of this comprehensive overview of recent advancements in the field.

Syllabus

Introduction
Prescribed curvature
Simonides 2018
Two years ago
Two parts
Plot a figure
Remarks
Outline
Geometric measure theory
Minimal hypersurfaces
First variation formula
AC functional
First variation argument
Mimax idea
Limit of time
Weak limits
Almost minimizing concept
Closed CMC surfaces
Noncompact manifold
Generalizing
MiMax Theorem
Multiplicity
Area Functional