12
Fachbereich
Institut für Mathematik
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Oberseminar Geometrische Analysis​​

Geometrische Analysis

Apr 29 2025
14:00

RM10 - 903

​Jonas Peteranderl (LMU München:  The sharp $\sigma_2$-curvature inequality on the sphere in quantitative form

Abstract: The goal of studying (quantitative) stability for sharp functional inequalities is to improve
them by adding terms involving the distance to the set of optimizers. We are interested in
non-Hilbertian settings where the bigger side of the inequality is not induced by an inner
product. As is well known, among all metrics on the sphere that are conformal to the
standard metric and have positive scalar curvature, the total σ2-curvature, normalized by
the volume, is uniquely (up to M¨obius transformations) minimized by the standard metric.
We show that if a metric almost minimizes, then it is almost the standard metric (up to
M¨obius transformations). Moreover, we measure this closeness in terms of Sobolev norms of
the conformal factor and obtain the optimal exponents for two different notions of distance
to the set of minimizers.
The talk is based on joint work with Rupert Frank.

Geometrische Analysis

Apr 22 2025
14:00

RM10 - 903

Adrian Spangenberger: Bewertungen auf Mannigfaltigkeiten

Vortrag zur Masterarbeit