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442505 VU The Plateau problem in the Calculus of Variations (2018W)

Continuous assessment of course work


Language: English



- Tuesday 4.September fom 9:15 to 12:00, HS05
- Wednesday, 5.September from 9:15 to 12:00, HS05
- Thursday, 6.September from 9:15 to 12:00, HS05
- Friday, 7.September from 9:15 to 12:00, HS05
- Monday, 10.September from 9:15 to 12:00, HS05
- Tuesday, 11.September from 9:15 to 12:00, HS05


Aims, contents and method of the course

The aim of the course is to give an overview of the main techniques for the Plateau problem, that is to find a surface with minimal area that spans a given boundary curve in ℝ^3. This problem dates back to the physical experiments of Joseph Plateau who tried to understand the possible configurations of soap films. From the mathematical point of view the problem is very hard and a lot of possible formulations are available: perhaps still today none of these answers is the answer to the original formulation by Plateau. In this course first of all I will briefly introduce the problem showing that, at least in the smooth case, if the first variation of the area vanishes then the surface must have zero mean curvature. Then I will describe how the classical solution by Douglas and Rado works, and I will pass to modern formulations of the problem in the context of geometric measure theory: finite perimeter sets approach, currents approach, and minimal sets approach. Possibly, some physical experiments with soap films could be done in order to clarify advantages and drawbacks of the approaches.

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

Association in the course directory


Last modified: Fr 31.08.2018 08:43