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EMBEDDING RIEMANNIAN MANIFOLDS VIA THEIR EIGENFUNCTIONS AND THEIR HEAT KERNEL
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 Title & Authors
EMBEDDING RIEMANNIAN MANIFOLDS VIA THEIR EIGENFUNCTIONS AND THEIR HEAT KERNEL
Abdalla, Hiba;
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 Abstract
In this paper, we give a generalization of the embeddings of Riemannian manifolds via their heat kernel and via a finite number of eigenfunctions. More precisely, we embed a family of Riemannian manifolds endowed with a time-dependent metric analytic in time into a Hilbert space via a finite number of eigenfunctions of the corresponding Laplacian. If furthermore the volume form on the manifold is constant with time, then we can construct an embedding with a complete eigenfunctions basis.
 Keywords
Riemannian manifold;Laplacian;eigenvalues/eigenfunctions;heat equation;embedding;
 Language
English
 Cited by
1.
Embeddings of Riemannian Manifolds with Heat Kernels and Eigenfunctions, Communications on Pure and Applied Mathematics, 2016, 69, 3, 478  crossref(new windwow)
2.
The embedding dimension of Laplacian eigenfunction maps, Applied and Computational Harmonic Analysis, 2014, 37, 3, 516  crossref(new windwow)
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