4 papers
A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions
Gabriel Khan, Soumyajit Saha, Malik Tuerkoen
In this paper, we establish a priori log-concavity estimates for the first Dirichlet eigenfunction of convex domains of a Riemannian manifold. Specifically, we focus on cases where…
Sum-of-Squares Programming for Ma-Trudinger-Wang Regularity of Optimal Transport Maps
Sachin Shivakumar, Georgiy A. Bondar, Gabriel Khan +1
For a given ground cost, approximating the Monge optimal transport map that pushes forward a given probability measure onto another has become a staple in several modern machine le…
Spectral Gap Estimates on Conformally Flat Manifolds
Gabriel Khan, Malik Tuerkoen
The fundamental gap is the difference between the first two Dirichlet eigenvalues of a Schrödinger operator (and the Laplacian, in particular). For horoconvex domains in hyperbolic…
Concavity Properties of Solutions of Elliptic Equations under Conformal Deformations
Gabriel Khan, Soumyajit Saha, Malik Tuerkoen
We study the Dirichlet problem for the weighted Schrödinger operator \[-Δu +Vu = λρu,\] where is a positive weighting function and is a potential. Such equations appear nat…