The doubling conjecture for positive scalar curvature

by Georg Frenck

Tuesday 21 May 2024, 16:00 → 18:00 Europe/Zurich

Sitzungszimmer (MI)

Any manifold with boundary admits a metric of positive scalar curvature (psc) by virtue of Gromov’s h-principle. Hence, one instead considers psc-metrics with suitable geometric boundary conditions, like mean convex, minimal or totally geodesic boundary. The doubling conjecture due to Rosenberg—Weinberger predicts that M admits a metric of positive scalar curvature with mean convex boundary if and only if the double of M admits a metric of positive scalar curvature. In this talk I will present a technique of proof which allows to prove this conjecture in many cases, provided, the boundary is connected. This is joint work with Bernhard Hanke.