3 papers
math.AP2025
On Poincaré constants related to isoperimetric problems in convex bodies
Dorin Bucur, Ilaria FragalÃ
For any convex set , we provide a lower bound for the inverse of the Poincaré constant in : it refines an inequality in terms of the diam…
math.SP2025
The geometric size of the fundamental gap
Vincenzo Amato, Dorin Bucur, Ilaria FragalÃ
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.AP2024
A sharp quantitative nonlinear Poincaré inequality on convex domains
Vincenzo Amato, Dorin Bucur, Ilaria FragalÃ
For any , we give a new inequality for the first nontrivial Neumann eigenvalue of the -Laplacian on a convex domain $Ω\subset \mathbb{R}^N…