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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…
math.DG2023
Modulus of Concavity and Fundamental Gap Estimates on Surfaces
Gabriel Khan, Malik Tuerkoen, Guofang Wei
The fundamental gap of a domain is the difference between the first two eigenvalues of the Laplace operator. In a series of recent and celebrated works, it was shown that for conve…