Nous étudions le spectre de l’opérateur de Laplace sur les ensembles algébriques et semi-algébriques dans .
The spectrum of the Laplace operator on algebraic and semialgebraic subsets in is studied and the number of small eigenvalues is estimated by the degree of .
@article{AIF_1992__42_1-2_249_0,
author = {Gromov, Mikhael},
title = {Spectral geometry of semi-algebraic sets},
journal = {Annales de l'Institut Fourier},
volume = {42},
year = {1992},
pages = {249-274},
doi = {10.5802/aif.1291},
mrnumber = {93i:58157},
zbl = {0759.58048},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1992__42_1-2_249_0}
}
Gromov, Mikhael. Spectral geometry of semi-algebraic sets. Annales de l'Institut Fourier, Tome 42 (1992) pp. 249-274. doi : 10.5802/aif.1291. http://gdmltest.u-ga.fr/item/AIF_1992__42_1-2_249_0/
[At] , Resolution of singularities and division of distributions, Comm. Pure Appl. Math., 23 (1970), 145-150. | MR 41 #815 | Zbl 0188.19405
[Ber] , Moduli over the ring of differential operators, Funct. Anal. and App.
[BerGel] , , Meromorphicity of the function pλ, Funct. Anal and Applic., (Russian), 3-1 (1969), 84-85.
[Bj] , Rings of differential operators, North-Holland Publ. Co. Math. Libr., 21 (1979). | MR 82g:32013 | Zbl 0499.13009
[Che1] , A lower bound for the smallest eigenvalue of the Laplacian, Problem in Analysis, A symposium in honor of Bochner (1970), Princeton, pp 195-199. | MR 53 #6645 | Zbl 0212.44903
[Che2] , On the Hodge theory of Riemannian pseudomanifolds, Proc. Symp. Pure Math., AMS Providence R.I., XXXVI (1980), 91-146. | MR 83a:58081 | Zbl 0461.58002
[Che3] , Spectral geometry of singular Riemannian spaces, J. Diff. Geom., 18-4 (1983), 575-657. | MR 85d:58083 | Zbl 0529.58034
[Gro1] , Paul Levy's isoperimetric inequality (1980) Preprint, IHES.
[Gro2] , Dimension, non-linear spectra and width, Springer Lecture Notes, 1317 (1988), 132-185. | MR 90d:58022 | Zbl 0664.41019
[Gro3] , Entropy, homology and semialgebraic geometry (after Yomdin), Astérisque, Soc. Math. France, 145-146 (1987), 225-241. | Numdam | MR 89f:58082 | Zbl 0611.58041
[Gro4] , Curvature, diameter and Betti numbers, Comm. Math. Helv., 56 (1981), 179-195. | MR 82k:53062 | Zbl 0467.53021
[Kho] , Fewnomials, Translation of Math. Monographs, V. 88, AMS, 1991. | Zbl 0728.12002
[Mil] , On the Betti numbers of real varieties, Proc. Am. Math. Soc., 15 (1964), 275-280. | MR 28 #4547 | Zbl 0123.38302
[Tho] , Sur l'homologie des variétés algébriques réelles. In Differential and Combinatorial Topology. A symposium in honor of M. Morse, Princeton University Press, 1965, pp. 252-265. | Zbl 0137.42503
[Yom] , Global bounds for the Betti numbers of regular fibers of differential mappings, Topology, 24-2 (1985), 145-152. | MR 87a:58030 | Zbl 0566.57014