Urs Lang: Katalogdaten im Herbstsemester 2018 |
| Name | Herr Prof. Dr. Urs Lang |
| Lehrgebiet | Mathematik |
| Adresse | Professur für Mathematik ETH Zürich, HG G 27.3 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telefon | +41 44 632 60 11 |
| urs.lang@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~lang |
| Departement | Mathematik |
| Beziehung | Ordentlicher Professor |
| Nummer | Titel | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|
| 401-4115-00L | Introduction to Geometric Measure Theory | 6 KP | 3V | U. Lang | |
| Kurzbeschreibung | Introduction to Geometric Measure Theory from a metric viewpoint. Contents: Lipschitz maps, differentiability, area and coarea formula, rectifiable sets, introduction to the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, normal currents, relation to BV functions, slicing, compactness theorem for integral currents and applications. | ||||
| Lernziel | |||||
| Inhalt | Extendability and differentiability of Lipschitz maps, metric differentiability, rectifiable sets, approximate tangent spaces, area and coarea formula, brief survey of the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, currents with finite mass and normal currents, relation to BV functions, rectifiable and integral currents, slicing, compactness theorem for integral currents and applications. | ||||
| Literatur | - Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces, 1995 - Herbert Federer, Geometric Measure Theory, 1969 - Leon Simon, Introduction to Geometric Measure Theory, 2014, web.stanford.edu/class/math285/ts-gmt.pdf - Luigi Ambrosio and Bernd Kirchheim, Currents in metric spaces, Acta math. 185 (2000), 1-80 - Urs Lang, Local currents in metric spaces, J. Geom. Anal. 21 (2011), 683-742 | ||||
| 401-5530-00L | Geometry Seminar  | 0 KP | 1K | M. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, Uni-Dozierende | |
| Kurzbeschreibung | Research colloquium | ||||
| Lernziel | |||||
| 406-2284-AAL | Measure and Integration Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen. | 6 KP | 13R | U. Lang | |
| Kurzbeschreibung | Introduction to the abstract measure theory and integration, including the following topics: Lebesgue measure and Lebesgue integral, Lp-spaces, convergence theorems, differentiation of measures, product measures (Fubini's theorem), abstract measures, Radon-Nikodym theorem, probabilistic language. | ||||
| Lernziel | Basic acquaintance with the theory of measure and integration, in particular, Lebesgue's measure and integral. | ||||
| Literatur | 1. Lecture notes by Professor Michael Struwe (http://www.math.ethz.ch/~struwe/Skripten/AnalysisIII-SS2007-18-4-08.pdf) 2. L. Evans and R.F. Gariepy "Measure theory and fine properties of functions" 3. Walter Rudin "Real and complex analysis" 4. R. Bartle The elements of Integration and Lebesgue Measure 5. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis. http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf | ||||