Universität Wien
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250133 VO Introduction to Geometric Measure Theory (2025S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
We 05.03. 13:15-14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

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Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 06.03. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.03. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 20.03. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 27.03. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.04. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.04. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 08.05. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.05. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.05. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.06. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.06. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.06. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The course is meant to introduce some of the foundational tools of geometric measure theory. Such tools find applications in several current research areas of analysis and geometry, e.g., in calculus of variations, harmonic analysis, global differential geometry, and analysis on metric spaces.

I expect to cover the following topics:
i) Recapitulation about key notions of measure theory; covering theorems.
ii) Hausdorff measures.
iii) Lipschitz functions; rectifiable sets; area and coarea formulas.
iv) Functions of bounded variation and sets of finite perimeter.
v) Introduction to regularity theory for perimeter minimizing sets.

Additional topics might be discussed, taking the audience's interests into account.

Prerequisites: Familiarity with basic functional analysis (duality, weak topologies, Riesz representation theorem), integration theory (with respect to abstract measures), Sobolev spaces and weak derivatives.

Assessment and permitted materials

Thorough 30-minute oral exam based on the content of the lectures.

Minimum requirements and assessment criteria

Examination topics

All course content is examinable.

Reading list

-Leon Simon: Introduction to Geometric Measure Theory, (ed. 2017). Notes freely available online.
-Luigi Ambrosio, Nicola Fusco, Diego Pallara: Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs. Oxford: Clarendon Press. xviii, 434 p. (2000).
-Lawrence C. Evans, Ronald F. Gariepy: Measure theory and fine properties of functions. 2nd revised ed. Textbooks in Mathematics. Boca Raton, FL: CRC Press. 309 p. (2015).
-Perti Mattila: Geometry of sets and measures in Euclidean spaces. Cambridge University Press, 1995.

Association in the course directory

MGEV;MSTV;MANV

Last modified: We 15.01.2025 15:26