5 papers
The monopolist's free boundary problem in the plane
Robert J. McCann, Cale Rankin, Kelvin Shuangjian Zhang
We study the Monopolist's problem with a focus on the free boundary separating bunched from unbunched consumers, especially in the plane, and give a full description of its solutio…
Convexity inequalities for eigenvalues and log-concavity of eigenfunctions
Paul Bryan, Julie Clutterbuck, Cale Rankin
We give simple new proofs of two well-known results for the Schrödinger operator: first, the Brunn--Minkowski inequality for Dirichlet eigenvalues and, second, the log-concavity o…
On the Hausdorff dimension and singularities of the monopolist's free boundary curve
Robert J. McCann, Lucas D. O'Brien, Cale Rankin
The simplest genuinely multidimensional monopolist's problem involves minimizing a linearly perturbed Dirichlet energy among nonnegative convex functions on an open domain $X \…
Bregman-Wasserstein divergence: geometry and applications
Amanjit Singh Kainth, Cale Rankin, Ting-Kam Leonard Wong
The Bregman-Wasserstein divergence is the optimal transport cost when the underlying cost function is given by a Bregman divergence, and arises naturally in fields such as statisti…
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…