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.
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.
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://www.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://www.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://www.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, Volume 61 (2011) no. 4, pp. 1557-1572. doi : 10.5802/aif.2651. http://www.numdam.org/articles/10.5802/aif.2651/
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