3 papers
math.AP2026
On the optimal sets in Pólya and Makai type inequalities
Vincenzo Amato, Nunzia Gavitone, Rossano Sannipoli
In this paper, we examine some shape functionals, introduced by Pólya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open an…
math.SP2026
On some functionals involving torsional rigidity, principal eigenvalue and perimeter
Vincenzo Amato, Carlo Nitsch, Cristina Trombetti +1
In this paper we study some relationships between the first Dirichlet eigenvalue and the torsional rigidity of a domain . We consider the problem of optimizing…
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…