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Introductory lectures on mean curvature flow and minimal surfaces

Course Type: 
PhD Course
Academic Year: 
2023-2024
Period: 
May-July
Duration: 
20 h
Description: 
  • Lesson 21/05: ROOM 134
  • Lesson 22/05: ROOM 133
  • Lesson 28/05: ROOM 
  • Lesson 29/05: ROOM 136

Program:

  • Boundary of sets and signed distance functions.
  • Mean curvature and second fundamental form.
  • First variation of area.
  • Gradient flow of area.
  • Smooth mean curvature flow: short-time existence theorem.
  • Examples of singularities formation in mean curvature flow.
  • The method of Almgren-Taylor-Wang and the De Giorgi minimizing movement method.
  • The Gamma-limit of De Giorgi and Modica-Mortola.
  • The Ginzburg-Landau (or Allen-Cahn) approximation of minimal surfaces and of mean curvature

First lecture:  This first lecture is aimed to introduce the course, and to fix the time schedule of the lectures with the interested students 

Location: 
TBC(to be checked)
Next Lectures: 

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