92 citations · 590 across the 51 of their papers we have counts for
55 papers
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…