Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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EMBEDDING RIEMANNIAN MANIFOLDS VIA THEIR EIGENFUNCTIONS AND THEIR HEAT KERNEL

  • Abdalla, Hiba (Universite de Grenoble 1 Institut Fourier Laboratoire de Mathematiques associe au CNRS)
  • Received : 2011.05.09
  • Published : 2012.09.30

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.

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Cited by

  1. Embeddings of Riemannian Manifolds with Heat Kernels and Eigenfunctions vol.69, pp.3, 2016, https://doi.org/10.1002/cpa.21565
  2. The embedding dimension of Laplacian eigenfunction maps vol.37, pp.3, 2014, https://doi.org/10.1016/j.acha.2014.03.002