Prescribing scalar curvatures: the negative case
Martin Mayer (Scuola Superiore Meridionale, Napoli)
- https://www.uni-giessen.de/de/fbz/fb07/fachgebiete/mathematik/mathematik/kalender/2022/2022-05-27
- Prescribing scalar curvatures: the negative case
- 2022-05-27T16:15:00+02:00
- 2022-05-27T17:15:00+02:00
- Martin Mayer (Scuola Superiore Meridionale, Napoli)
27.05.2022 von 16:15 bis 17:15 (Europe/Berlin / UTC200)
Hörsaal (1. Stock, Raum 111) im Mathematischen Institut, Arndtstraße 2
Abstract:
The problem of prescribing conformally the scalar curvature on a closed manifold of negative Yamabe invariant is always solvable, if the function to be prescribed is strictly negative, while sufficient and necessary conditions are known in the case that function is non positive. Still in the case of a negative Yamabe invariant, Rauzy (Trans. Amer. Math. Soc. 1995) showed solvability, if the function to be prescribed is not too positive, as quantified by Aubin-Bismuth (J.
Funct. Anal. 1997) later on. In this talk we will review these results variationally and shed some light on the case, when Rauzy's conditions fail. This talk is joint work with Chaona Zhu.