Universität des Saarlandes  


Minimal surfaces and the calculus of variations

  1. The latest news.
    1. First meeting with some preliminary discussion: Tuesday, October 16th, 12.15, SR5, E2 4.

  2. Lecture.
    1. On Tuesdays, 12-14, SR5, E2 4

    2. Credit Points: 4,5

    3. Lecturer: Prof. Dr. Michael Bildhauer, Building E2 4, Room 102, Phone: 302-2384.

  3. Contents.
    The study and understanding of minimal surfaces, for instance soap films, relies on a series of different techniques from pure and applied mathematics. In particular we have to discuss the following fields:

    1. Partial differential equations
    2. Calculus of variations (as one main block)
    3. Differential geometry
    4. Complex analysis

    With this tools we finally discuss the famous Plateau Problem

    The lecture will be self-contained, i.e. no particular knowledge on the above mentioned fields is required. Nevertheless, the students are expected to be familiar with the calculus of several variables (in particular Analysis 2) and with linear algebra.

  4. References.
    Skript von Prof. Fuchs

  5. Exercises: Mi, 8.30-10.00, Zeichensaal

  6. Mi., 05.12.2012: Frenetsches Dreibein..., isoperimetrische Ungleichung

    Mi., 12.12.2012: Aufgaben zur lokalen Kurventheorie, Satz von Liouville, geometrische Definition des Flächeninhalts

    Mi., 19.12.2012: Asymptoten- Krümmungslinien, Normalschnitt, Geodätische

    Mi., 09.01.2013: Geodätische auf Rotationsflächen, Fundamentallemma, Kontinuitäsgleichung

    Mi., 16.01.2013: hängender Tropfen, Erhaltungssätze, Frei Otto