Content

This lecture series will give a sample of the diverse occurrences of surfaces in analysis, geometry and physics. In particular, the following topics will be covered.

1. Shape and sound -- spectral theory of surfaces (C. Bär).

2. Geometric inequalities (J. Metzger).

3. Hypersurfaces with singularities -- Caccioppoli sets (U. Menne).

4. Surfaces viewed as paths: an introduction to bosonic string theory (S. Paycha).

References

References will be announced in the lecture. Amongst them the following.

• Peter Buser. Geometry and spectra of compact Riemann surfaces, volume 106 of Progress in Mathematics. Birkhäuser Boston, Inc., Boston, MA, 1992.
• Enrico Giusti. Minimal surfaces and functions of bounded variation, volume 80 of Monographs in Mathematics. Birkhäuser Verlag, Basel, 1984. URL: dx.doi.org/10.1007/978-1-4684-9486-0.
• Jürgen Jost. Bosonic strings: a mathematical treatment, volume 21 of AMS/IP Studies in Advanced Mathematics. American Mathematical Society, Providence, RI; International Press, Somerville, MA, 2001.

Departmental course description ("Kommentiertes Vorlesungsverzeichnis (KVV)")

Link to the KVV.

Moodle

Announcements about the course and exercise sheet distribution will happen thru the Moodle Platform.