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math.AP2018★ 5 cited
Localization of Neumann Eigenfunctions near Irregular Boundaries
Peter W. Jones, Stefan Steinerberger
It has been empirically observed that eigenfunctions of Laplace's equation with Neumann boundary conditions sometimes localize near the boundary of the domain if that bou…
math.AP2007★ 16 cited
Universal local parametrizations via heat kernels and eigenfunctions of the Laplacian
Peter W. Jones, Mauro Maggioni, Raanan Schul
We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g. w…