Collection Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
Organizer(s)
Date(s)
26/04/2024
Compactness of conformal metric with a critical integrability assumption
This is a joint work with Clara Aldana (Luxembourg) and Samuel Tapie (Nantes).In 1993, M. Gursky has shown a compactness result in $C^{1,\alpha}$ for conformal metrics $g=e^{2f}g_0$ of unit volume and uniform $L^p$-bound on the full curvature tensor (where $p>dim/2$). We will describe what kind of compactness theorem can be obtained for conformal metric with unit volume and uniform $L^{dim/2}$ bound on the scalar curvature.
