Convergence of Riemannian manifolds and Laplace operators. I
Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1219-1257.

We study the spectral convergence of compact Riemannian manifolds in relation with the Gromov-Hausdorff distance and discuss the geodesic distances and the energy forms of the limit spaces.

Nous étudions la convergence spectrale des variétés riemanniennes compactes par rapport à la distance de Gromov-Hausdorff et discutons des distances géodésiques et des formes d'énergie des espaces de limites.

DOI: 10.5802/aif.1916
Classification: 53C21,  58D17,  58J50
Keywords: Laplace operator, energy form, heat kernel, spectral convergence, Gromov-Hausdorff distance
Kasue, Atsushi 1

1 Osaka City University, Department of Mathematics, Sugimoto, Sumiyoshi, Osaka 558-8585 (Japon) et Kanazawa University, Department of Mathematics, Kanazawa 920-1192 (Japon)
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Kasue, Atsushi. Convergence of Riemannian manifolds and Laplace operators. I. Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1219-1257. doi : 10.5802/aif.1916. http://www.numdam.org/articles/10.5802/aif.1916/

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