3 papers
math.DG2025
Quaternionic-Kähler manifolds with nonnegative sectional curvature
S. Brendle, U. Semmelmann
We show that a compact quaternionic-Kähler manifold with positive scalar curvature and nonnegative sectional curvature is isometric to a symmetric space. This extends a classical t…
math.DG2023
Scalar curvature rigidity of convex polytopes
S. Brendle
We prove a scalar curvature rigidity theorem for convex polytopes. The proof uses the Fredholm theory for Dirac operators on manifolds with boundary. A variant of a theorem of Feff…
math.DG2016
Ricci flow with surgery in higher dimensions
S. Brendle
We present a new curvature condition which is preserved by the Ricci flow in higher dimensions. For initial metrics satisfying this condition, we establish a higher dimensional ver…