92 citations · 590 across the 51 of their papers we have counts for
52 papers · 1 filter
Ricci flow on manifolds with positive isotropic curvature in all dimensions
Simon Brendle, Raphael Tsiamis
We extend the classification of manifolds with positive isotropic curvature to all dimensions . This result also completes the classification of uniformly positive isotro…
Scalar curvature rigidity of warped product metrics
Christian Baer, Simon Brendle, Bernhard Hanke +1
We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This…
Rigidity results for initial data sets satisfying the dominant energy condition
Christian Baer, Simon Brendle, Tsz-Kiu Aaron Chow +1
Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energ…
A generalization of Geroch's conjecture
Simon Brendle, Sven Hirsch, Florian Johne
The Theorem of Bonnet--Myers implies that manifolds with topology do not admit a metric of positive Ricci curvature, while the resolution of Geroch's…
Proof of the Michael-Simon-Sobolev inequality using optimal transport
S. Brendle, M. Eichmair
We give an alternative proof of the Michael-Simon-Sobolev inequality using techniques from optimal transport. The inequality is sharp for submanifolds of codimension .
Singularity models in the three-dimensional Ricci flow
S. Brendle
The Ricci flow is a natural evolution equation for Riemannian metrics on a given manifold. The main goal is to understand singularity formation. In his spectacular 2002 breakthroug…