[Limite inférieure de la courbure de Ricci qui donne un nombre de spectre discret infini]
Ce document traite de la question si le spectre discret de l’opérateur de Laplace-Beltrami est infini ou fini. La ligne de démarcation du comportement des courbures de ce problème sera complètement déterminée.
This paper discusses the question whether the discrete spectrum of the Laplace-Beltrami operator is infinite or finite. The borderline-behavior of the curvatures for this problem will be completely determined.
Keywords: Laplace-Beltrami operator, discrete spectrum, Ricci curvature
Mot clés : opérateur de Laplace-Beltrami, spectre discret, courbure de Ricci
@article{AIF_2011__61_4_1557_0,
author = {Kumura, Hironori},
title = {The lower bound of the {Ricci} curvature that yields an infinite discrete spectrum of the {Laplacian}},
journal = {Annales de l'Institut Fourier},
pages = {1557--1572},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {61},
number = {4},
year = {2011},
doi = {10.5802/aif.2651},
zbl = {1252.58017},
mrnumber = {2951504},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.2651/}
}
TY - JOUR AU - Kumura, Hironori TI - The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian JO - Annales de l'Institut Fourier PY - 2011 SP - 1557 EP - 1572 VL - 61 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2651/ DO - 10.5802/aif.2651 LA - en ID - AIF_2011__61_4_1557_0 ER -
%0 Journal Article %A Kumura, Hironori %T The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian %J Annales de l'Institut Fourier %D 2011 %P 1557-1572 %V 61 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2651/ %R 10.5802/aif.2651 %G en %F AIF_2011__61_4_1557_0
Kumura, Hironori. The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1557-1572. doi : 10.5802/aif.2651. http://archive.numdam.org/articles/10.5802/aif.2651/
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