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401-3588-00L 10 Credits BSC , DR , MSC D-USYS , D-MAVT , D-MTEC , D-MATH , D-BIOL , D-CHAB

Partial Differential Equations in Geometry

Lecturers & Examiners: Prof. em. Dr. Dietmar A. Salamon
VVZ CR n/a

Last Updated: 2026-02-05 15:19:32

Abstract

Goal of the lecture course is to give an introduction to elliptic PDEsand some of their applications in geometry

Objective

Introduction to elliptic PDEs and some of their applications in geometry

Content

Part 1: PDEs Sobolev spaces, embedding theorems, the Calderon-Zygmund inequality, Lp-theory for 2nd order elliptic operators Part 2: Applications in Geometry Hodge theory, the uniformization theorem (as time allows: Cauchy-Riemann operators, Teichmueller space, diffeomorphism groups of Riemann surfaces)

Resources

Literature

Gilbarg-Trudinger, Elliptic PDEs of Second Order Adams-Fournier, Sobolev Spaces, 2nd edition, Giaquinta-Martinazzi, An introduction to the regularity for elliptic systems, harmonic maps, and minimal graphs McDuff-Salamon, J-holomorphic Curves and Symplectic Topology, Appendix B Guillemin-Pollack, Differential Topology (background material on manifolds and differential forms)

General Information

Language
English
Levels
BSC , DR , MSC

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Partial Differential Equations in Geometry
  • Tue 08:15-10:00 (HG G 5)
  • Thu 10:15-12:00 (HG E 1.2)
4 h weekly
exercise Partial Differential Equations in Geometry
  • Wed 16:15-17:00 (HG D 5.1)
  • Wed 16:15-17:00 (HG D 5.3)
  • Wed 16:15-17:00 (HG E 1.1)
1 h weekly

Offered In