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401-5003-57L DR D-USYS , D-BAUG , D-MAVT , D-INFK , D-MTEC , D-MATH , D-BIOL , D-GESS , D-ITET , D-ARCH , D-CHAB

The Willmore Functional

Lecturers: Prof. Dr. Ernst Kuwert
VVZ CR n/a

Last Updated: 2026-02-05 15:14:58

Abstract

"Nachdiplomvorlesung"

Content

For any two-dimensional surface f : Sigma -> R^n, the Willmore functional is given by the the following integral over Sigma W(f)= 1/4 Integral |H|^2 dµ where H is the mean curvature vector and µ is the area measure. The central geometric feature of the functional is its invariance under the Möbius group of R^n . The corresponding Euler Lagrange equation is a fourth order quasilinear elliptic system, whose solutions are called Willmore surfaces. The lecture starts with classical material on the geometry of the functional, including basic formulae and inequalities due to Willmore and Li-Yau. The main focus will then be on analytic questions which have been addressed in joint work with Reiner Schätzle (Universität Tübingen) in the last years. Specifically, we plan to discuss the Willmore flow, the removability of point singularities in codimension one Willmore surfaces and, if time permits, a recent bilipschitz estimate for surfaces of low Willmore energy. The course requires no prerequisites. At a later point, we will need one or two results from the literature which will be stated without proof.

General Information

Language
English
Levels
DR

Examination

Type
no performance assessment

Course Components

Type Title Time & Place Hours
lecture The Willmore Functional
Beginn: 03.10.2007
  • Wed 14:15-16:00 (HG G 43)
2 h weekly

Offered In