Dr. James D.E. Grant
james.grant@univie.ac.at
Fakultät für Mathematik
Universität Wien
1090-Wien
Telephone | 01 4277 50632 |
Fax | 01 4277 50620 |
To introduce some modern results in geometric analysis. Particular goals are to discuss the following topics:
It is assumed that you will be familiar with the material contained in the courses Differential Geometry I and Differential Geometry II. The material contained in Global Lorentzian Geometry 1 would be useful but (probably) not essential.
I will be in my office, C 237, Monday 9-10am. You may drop by then to ask questions. If you wish to see me at any other time, please email me so that we can make an appointment.
The course should be quite self-contained, and I will make a set of typed notes available as the course progresses. Most of the material is quite modern, and cannot be found in a single textbook. The initial parts on the positive mass/energy theorem will follow the paper of Parker and Taubes:
More details concerning Clifford algebras and some details of Witten's proof of the positive mass/energy theorem may be found in
although this is not really a place that I would recommending learning this (or any other) material from. There is also the review article
although this assumes a fair amount of background knowledge.
The connection between the Yamabe problem and Perelman functional was pointed out in the paper
The original paper by Perelman may be found at
There are now various papers, books and websites dedicated to expanding and explaining Perelman's papers on the Geometrisation Conjecture. A good place to start, if you want to find out more about this topic, is the Kleiner-Lott website.