Concavity for elliptic and parabolic equations in complex projective space
S Aryan, MB Law - arXiv preprint arXiv:2403.16783, 2024 - arxiv.org
We establish a concavity principle for solutions to elliptic and parabolic equations on
complex projective space, generalizing the results of Langford and Scheuer. To our …
complex projective space, generalizing the results of Langford and Scheuer. To our …
Spectral Gap Estimates on Conformally Flat Manifolds
G Khan, M Tuerkoen - arXiv preprint arXiv:2404.15645, 2024 - arxiv.org
The fundamental gap is the difference between the first two Dirichlet eigenvalues of a Schr\"
odinger operator (and the Laplacian, in particular). For horoconvex domains in hyperbolic …
odinger operator (and the Laplacian, in particular). For horoconvex domains in hyperbolic …
A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions
G Khan, S Saha, M Tuerkoen - arXiv preprint arXiv:2501.03504, 2025 - arxiv.org
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 the …
of convex domains of a Riemannian manifold. Specifically, we focus on cases where the …