Embedding Riemannian manifolds via their eigenfunctions and their heat kernel
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 939-947
https://doi.org/10.4134/BKMS.2012.49.5.939
Printed September 30, 2012
Hiba Abdallah
Laboratoire de Math\'ematiques associ\'e au CNRS
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
MSC numbers : 47B40, 53B21, 54A20, 58A32, 58C25, 58C40
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