442505 VU The Plateau problem in the Calculus of Variations (2018W)
Continuous assessment of course work
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Language: English
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Classes
- 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
Information
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.
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Minimum requirements and assessment criteria
Examination topics
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Association in the course directory
MANV; MAMV;
Last modified: Fr 31.08.2018 08:43