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math.SP2026
Planar Dirichlet eigenvalue bounds from a trace identity
Romain Speciel
We prove an asymptotically sharp lower bound for the eigenvalues of the Dirichlet Laplacian on bounded open sets in the plane with area . The proof employs a trace ident…
math.SP2026
An inverse problem on eigenfunction triple products
Carl Schildkraut, Romain Speciel
On a connected closed smooth Riemannian manifold, the algebraic structure of the Laplace eigenfunctions, as described by eigenfunction triple products, uniquely determines the geom…
math.SP2026
Geometric rigidity from the Dirichlet-to-Neumann operator
Romain Speciel
The analytic properties of the Dirichlet-to-Neumann operator reflect the geometry of the underlying manifold. As a guiding example of this relationship, consider the Euclidean unit…