CORDIS Project
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This project aims to explore the relationship between the shape of geometric domains and their Laplace spectra. It seeks to prove local spectral rigidity for convex planar domains and Riemannian manifolds, developing tools to solve inverse problems in geometry.
In 1911, Hermann Weyl proved the remarkable asymptotic formula describing distribution of (large) eigenvalues of the Dirichlet Laplacian in a bounded domain Ω ⊂ RdN (λ) = (2π)−d ωd Vol(Ω) λd/2(1 + o(1))as λ → +∞. where N (λ) is the number
of eigenvalues of the Laplacian spectrum, which are less than λ, ωd is a volume of the unit ball in Rd, Vol(Ω) is the volume of Ω, and the Laplace spectrum of a domain Ω is defined as the set of positive real numbers λ (with
multiplicities) that satisfy the e…
INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
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