Mean Curvature Courses and Certifications

International Mathematical Union

Entropy in Mean Curvature Flow

Explore entropy in hypersurfaces and its role in mean curvature flow. Survey recent progress on conjectures about sharp lower bounds and extensions in geometric complexity.

• YouTube
• 43 minutes
• On-Demand
• Free Video

ICTP Mathematics

Phase-Field Models for Motion by Mean Curvature - Lecture 2

Explore phase-field models for motion by mean curvature, covering topics like skew symmetry, levelsets, distance functions, and classical statements with expert Panagiotis Souganidis.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

ICTP Mathematics

Singularities of the Mean Curvature Flow of Mean Convex Hypersurfaces - Lecture 5

Explore singularities in mean curvature flow of convex hypersurfaces, covering max inequality, weak solutions, surgeries, and Type 2 singularities with intuitive explanations.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Euclidean and Lorentz-Minkowski 3-Space - Lecture 1

Explore zero mean curvature surfaces in Euclidean and Lorentz-Minkowski spaces, covering fundamental concepts, variations, stability, and examples of minimal surfaces with diverse properties and geometries.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Society for Industrial and Applied Mathematics

Mean Curvature Flow, Neural Networks, and Applications

Explore mean curvature flow's applications in image processing, data science, and biology. Learn how neural networks can approximate interface evolutions for non-oriented surfaces, with applications to Steiner and Plateau problems.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Conference Talk

Society for Industrial and Applied Mathematics

Directed Mean Curvature Flow in Noisy Environment

Explore directed mean curvature flow in noisy environments and its connection to the KPZ equation through advanced mathematical analysis and stochastic PDEs.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

BIMSA

On the Enclosed Volume of Constant Mean Curvature Surfaces in the 3-Sphere and Euclidean 3-Space

Explore constant mean curvature surfaces in 3D spaces, computing area and enclosed volume using flat connection invariants. Joint work insights included.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

BIMSA

Recent Progress on Self-Expanders of Mean Curvature Flow and Applications

Explore recent advancements in self-expanders of mean curvature flow, their role in modeling singularities, and applications in geometric analysis.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

BIMSA

Generic Dynamics of the Mean Curvature Flows

Explore generic dynamics of mean curvature flows, including perturbation of shrinkers and isolatedness of cylindrical singularities in hypersurface evolution.

• YouTube
• 47 minutes
• On-Demand
• Free Video

BIMSA

Recent Progress on Minimal and Constant Mean Curvature Surfaces

Explore recent advancements in the existence theory of minimal and constant mean curvature surfaces, surveying cutting-edge developments in this mathematical field.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Centre de recherches mathématiques - CRM

An Excursion into Mean Curvature Flow

Explore mean curvature flow's regularity theory, focusing on distinctions between one-dimensional and higher-dimensional flows in this geometric analysis lecture.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Recent Developments in Constant Mean Curvature Hypersurfaces - Part II

Explore recent developments in constant mean curvature hypersurfaces, focusing on min-max theorems and the half-volume spectrum. Gain insights into advanced geometric analysis concepts.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Recent Developments in Constant Mean Curvature Hypersurfaces - Part I

Explore recent developments in constant mean curvature hypersurfaces, focusing on existence theory using min-max methods and discussing open problems in the field.

• YouTube
• 47 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Lorentz Minkowski Spaces - Lecture 3

Explore zero mean curvature surfaces in Lorentz-Minkowski spaces with expert Shoichi Fujimori. Delve into advanced geometric concepts and their applications in this specialized lecture.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Zero Mean Curvature Surfaces in Lorentz Minkowski Spaces - Lecture 2

Explore zero mean curvature surfaces in Lorentz-Minkowski spaces with expert Shoichi Fujimori. Delve into advanced geometric concepts and their applications in this specialized lecture.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video