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Positive mass theorem and application to the Yamabe problem Semester
SoSe 2023
Lecturer
Bernd Ammann
Type of course (Veranstaltungsart)
Vorlesung
German title
Das positive Masse-Theorem und Anwendung auf das Yamabe-Problem
Contents
The lecture will be given in English as soon as there is at least one Non-German speaking participant.
The content of the lecture is the positive mass theorem and its application to the Yamabe problem. The lecture thus has two goals:
- Explain the role of the ADM mass in general relativity. Roughly speaking the ADM mass describes the mass of a system of some stars and black holes in a universe that is asymptotically flat at infinity in general relativity. It may be extended to the ADM energy-momentum vector. The positive mass theorem (PMT) says: if the mass density of the space-time is non-negative, then its total mass is non-negative as well.
- Apply this to the Yamabe problem: in the winter term 2022/23 I gave a lecture
"Geometric partial differential equations on manifolds (Yamabe Problem)" in which the Yamabe problem was solved, assuming the Aubin-Schoen inequality. This inequality follows easily from the positive mass theorem.
Thus, there might be at least two reasons, why students can be interested in this lecture: understand the positive mass theorem, its significance in general relativity and its proofs. Or to see the last missing step to solve the Yamabe problem. The precise structure of the lecture, in particular the weight of these two parts, will thus depend on the audience.
Thus, I do not require that the audience has followed the lecture about the Yamabe problem, but if you have, you will have an additional motivation. The lecture will be adjusted accordingly.
Literature
Further literatur will be published on the web page.
Recommended previous knowledge
Differential geometry (Riemannian manifolds)
Time/Date
Di 10-12
Location
M101
Course homepage
http://www.mathematik.uni-regensburg.de/ammann/lehre/2023s_yamabe2/
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)
Registration- Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)- Oral examination (without grade): Duration: 30 minutes, Date: individually arranged
Examination (Prüfungsleistungen)- Oral exam: Duration: 30 minutes, Date: individually arranged, re-exam: Date:
Modules
BV, MV, MGAGeo, MAngAn
ECTS
3
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