6 papers
Payne's nodal line conjecture fails on doubly-connected planar domains
Pedro Freitas, Roméo Leylekian
We present examples of bounded planar domains with one single hole for which the nodal line of a second Dirichlet eigenfunction is closed and does not touch the boundary. This show…
Extremal problems for clamped plates under tension
Pedro Freitas, Roméo Leylekian
We address extremum problems for spectral quantities associated with operators of the form with Dirichlet boundary conditions, for non-negative values of . The focus is…
Pólya's conjecture on
Pedro Freitas, Rui Wang
We study the area ranges where the two possible isoperimetric domains on the infinite cylinder , namely, geodesic disks and cylindrical strips of the form…
Hermite's letters to Francisco Gomes Teixeira
Pedro J. Freitas
It is well known that Charles Hermite kept an intense correspondence with many of the word's leading mathematicians of his time. This paper focuses on Hermite's letters to Francisc…
On the (growing) gap between Dirichlet and Neumann eigenvalues
Pedro Freitas, Miguel Gama
We provide an answer to a question raised by Levine and Weinberger in their paper concerning the difference between Dirichlet and Neumann eigenvalues of the Laplacian on bou…
Unbounded planar domains whose second nodal line does not touch the boundary
P. Freitas, D. Krejcirik
We show the existence of simply-connected unbounded planar domains for which the second nodal line of the Dirichlet Laplacian does not touch the boundary.