4 papers
On fill-ins with scalar curvature bounded from below and an inequality of Hijazi-Montiel-Roldán
Simon Brendle, Raphael Tsiamis, Yipeng Wang
We consider fill-ins of spin manifolds with scalar curvature bounded by . Gromov proposed a conjecture relating the infimum of the mean curvature of such a fill-in to the…
The isoperimetric inequality
Simon Brendle, Michael Eichmair
We discuss several classical and recent proofs of the isoperimetric inequality and the Sobolev inequality.
Eigenvalue estimates on shrinkers
S. Brendle, R. Tsiamis
We prove an eigenvalue estimate which holds on every properly embedded shrinker for mean curvature flow. This generalizes earlier work of Ding and Xin to the noncompact case.
A geometric approach to apriori estimates for optimal transport maps
Simon Brendle, Flavien Léger, Robert J. McCann +1
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This tr…