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math.DG2024
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…
math.DG2024
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…