5 citations · 10 across the 13 of their papers we have counts for
13 papers
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 of…
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 \…
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…
JKO schemes with general transport costs
Cale Rankin, Ting-Kam Leonard Wong
We modify the JKO scheme, which is a time discretization of Wasserstein gradient flows, by replacing the Wasserstein distance with more general transport costs on manifolds. We sho…
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…
regularity for principal-agent problems
Robert J. McCann, Cale Rankin, Kelvin Shuangjian Zhang
We prove the interior regularity of the indirect utilities which solve a subclass of principal-agent problems originally considered by Figalli, Kim, and McCann. Our appro…
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 remark on the geometric interpretation of the A3w condition from optimal transport
Cale Rankin
We provide a geometric interpretation of the well known A3w condition for regularity of optimal transport maps.
First and second derivative Hölder estimates for generated Jacobian equations
Cale Rankin
We prove two Hölder regularity results for solutions of generated Jacobian equations. First, that under the A3 condition and the assumption of nonnegative valued data solutio…
Regularity and uniqueness results for generated Jacobian equations
Cale Rankin
This is a PhD thesis about generated Jacobian equations; our purpose is twofold. First, we provide an introduction to these equations, whilst, at the same time, collating some resu…
Strict -convexity for generated Jacobian equations with applications to global regularity
Cale Rankin
This article has two purposes. The first is to prove solutions of the second boundary value problem for generated Jacobian equations are strictly -convex. The second is to prove…
Strict convexity and regularity of solutions to generated Jacobian equations in dimension two
Cale Rankin
We present a proof of strict -convexity in 2D for solutions of generated Jacobian equations with a -Monge-Ampère measure bounded away from 0. Subsequently this implies …
Distinct solutions to generated Jacobian equations cannot intersect
Cale Rankin
We prove that if two solutions of the second boundary value problem for the generated Jacobian equation intersect in then they are the same solution. In addition w…