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math.DG2023
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…
math.DG2023
On Gromov's rigidity theorem for polytopes with acute angles
S. Brendle, Y. Wang
In his ``Four Lectures", Gromov conjectured a scalar curvature extremality property of convex polytopes. Moreover, Gromov outlined a proof of the conjecture in the special case whe…