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Creators/Authors contains: "Brendle, Simon"

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  1. ; (, Notices of the American Mathematical Society)
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  2. (, Inventiones mathematicae)
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  3. ; ; ; (, Symmetry, Integrability and Geometry: Methods and Applications)
    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 generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry. 
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  4. ; ; (, Communications on Pure and Applied Mathematics)
    Abstract 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 conjecture implies that the torus does not admit a metric of positive scalar curvature. In this work we introduce a new notion of curvature interpolating between Ricci and scalar curvature (so‐calledm‐intermediate curvature), and use stable weighted slicings to show that for and the manifolds do not admit a metric of positivem‐intermediate curvature. 
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  5. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract We give an alternative proof of the Michael–Simon–Sobolev inequality using techniques from optimal transport. The inequality is sharp for submanifolds of codimension 2. 
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  6. (, Communications on Pure and Applied Mathematics)
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  7. (, Communications on Pure and Applied Mathematics)
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  8. ; ; ; (, Communications on Pure and Applied Mathematics)
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  9. ; ; (, Inventiones mathematicae)
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  10. (, Journal of the American Mathematical Society)
    null (Ed.)
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