7 papers
Sharp Quantitative Stability of the Dirichlet spectrum near the ball
Dorin Bucur, Jimmy Lamboley, Mickaël Nahon +1
Let be an open set with the same volume as the unit ball and let be the -th eigenvalue of the Laplace operator of with Dirichlet boun…
Optimal domains for the Cheeger inequality
Dorin Bucur, Giuseppe Buttazzo, Alexis de Villeroché
In this paper we consider the scale invariant shape functional where and (respect…
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…
Spherical caps do not always maximize Neumann eigenvalues on the sphere
Dorin Bucur, Richard S. Laugesen, Eloi Martinet +1
We prove the existence of an open set for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic…
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…
On localisation of eigenfunctions of the Laplace operator
Michiel van den Berg, Dorin Bucur
We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a unif…