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.
Keywords: Laplace operator, energy form, heat kernel, spectral convergence, Gromov-Hausdorff distance
Mot clés : opérateur de Laplace, forme d'énergie, noyau de la chaleur, convergence spectrale, distance de Gromov-Hausdorff
@article{AIF_2002__52_4_1219_0, author = {Kasue, Atsushi}, title = {Convergence of {Riemannian} manifolds and {Laplace} operators. {I}}, journal = {Annales de l'Institut Fourier}, pages = {1219--1257}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {4}, year = {2002}, doi = {10.5802/aif.1916}, mrnumber = {1927079}, zbl = {1040.53053}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1916/} }
TY - JOUR AU - Kasue, Atsushi TI - Convergence of Riemannian manifolds and Laplace operators. I JO - Annales de l'Institut Fourier PY - 2002 SP - 1219 EP - 1257 VL - 52 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1916/ DO - 10.5802/aif.1916 LA - en ID - AIF_2002__52_4_1219_0 ER -
%0 Journal Article %A Kasue, Atsushi %T Convergence of Riemannian manifolds and Laplace operators. I %J Annales de l'Institut Fourier %D 2002 %P 1219-1257 %V 52 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1916/ %R 10.5802/aif.1916 %G en %F AIF_2002__52_4_1219_0
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://archive.numdam.org/articles/10.5802/aif.1916/
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