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The geometric size of the fundamental gap
Vincenzo Amato, Dorin Bucur, Ilaria Fragalà
The fundamental gap conjecture proved by Andrews and Clutterbuck in 2011 provides the sharp lower bound for the difference between the first two Dirichlet Laplacian eigenvalues in…
math.SP2024
On the torsion function for simply connected, open sets in
Michiel van den Berg, Dorin Bucur
For an open set $\Om \subset \R^2$ let $λ(\Om)$ denote the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Om)$. Let $w_\Om$ be the torsion function for $\Om$, an…