Tristan Rivière: Katalogdaten im Frühjahrssemester 2016 |
Name | Herr Prof. Dr. Tristan Rivière |
Lehrgebiet | Mathematik |
Adresse | Professur für Mathematik ETH Zürich, HG G 48.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
Telefon | +41 44 632 06 71 |
tristan.riviere@math.ethz.ch | |
URL | http://www.math.ethz.ch/~triviere |
Departement | Mathematik |
Beziehung | Ordentlicher Professor |
Nummer | Titel | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|
401-4530-16L | Min-Max Methods for the Constructions of Minimal Surfaces | 4 KP | 2S | T. Rivière | |
Kurzbeschreibung | In the proposed seminar we shall concentrate on the various minmax constructions of minimal surfaces in closed manifolds. | ||||
Lernziel | |||||
Inhalt | The study of minimal surfaces takes its origins in the works of Euler and Bernoulli from the XVIIIth century. Since these very early times, minimal surfaces have become central objects in mathematics much beyond the field of geometry *sticto sensu* with applications in analysis, in applied mathematics, in theoretical physics and natural sciences in general. Despite its venerable age the calculus of variations of the area functional is still a very active area of research with important developments that took place in the last decades. In the proposed seminar we shall concentrate on the various *minmax* constructions of minimal surfaces in closed manifolds. We shall first present the *parametric approach* of Colding and Minicozzi extending to two dimensions the original strategy of Birkhoff from 1915 of *sweep outs* and *curve shortening* procedure. In the second part of the seminar we will present the tools from *geometric measure theory* developed mostly by Allard, Almgren and Pitts for constructing minimal codimension 1 surfaces of non zero indices. This will naturally bring us to the recent existence results of Marques and Neves. Finally, if time permits, we will also cover the more recent strategy of *viscous approximations* of *minmax procedures* for two dimensional surfaces. | ||||
Literatur | 1) T.Colding and W.Minicozzi ''A course in Minimal Surfaces'' AMS (2011). 2) L.Simon ''Lectures on Geometric Measure Theory'' Australian National University (1983). 3) More bibliography will be given during the course of the seminar. | ||||
Voraussetzungen / Besonderes | Prerequisites : FA I + II, DG I + II and elementary notions from Elliptic PDE and Calculus of Variations from the book of Michael Struwe. | ||||
401-5350-00L | Analysis Seminar | 0 KP | 1K | M. Struwe, F. Da Lio, N. Hungerbühler, T. Kappeler, T. Rivière, D. A. Salamon | |
Kurzbeschreibung | Forschungskolloquium | ||||
Lernziel | |||||
Inhalt | Research seminar in Analysis |