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 .
Nous étudions le spectre de l’opérateur de Laplace sur les ensembles algébriques et semi-algébriques dans .
@article{AIF_1992__42_1-2_249_0,
author = {Gromov, Mikhael},
title = {Spectral geometry of semi-algebraic sets},
journal = {Annales de l'Institut Fourier},
pages = {249--274},
year = {1992},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {42},
number = {1-2},
doi = {10.5802/aif.1291},
mrnumber = {93i:58157},
zbl = {0759.58048},
language = {en},
url = {https://www.numdam.org/articles/10.5802/aif.1291/}
}
TY - JOUR AU - Gromov, Mikhael TI - Spectral geometry of semi-algebraic sets JO - Annales de l'Institut Fourier PY - 1992 SP - 249 EP - 274 VL - 42 IS - 1-2 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.1291/ DO - 10.5802/aif.1291 LA - en ID - AIF_1992__42_1-2_249_0 ER -
Gromov, Mikhael. Spectral geometry of semi-algebraic sets. Annales de l'Institut Fourier, …, Tome 42 (1992) no. 1-2, pp. 249-274. doi: 10.5802/aif.1291
[At] , Resolution of singularities and division of distributions, Comm. Pure Appl. Math., 23 (1970), 145-150. | Zbl | MR
[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). | Zbl | MR
[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. | Zbl | MR
[Che2] , On the Hodge theory of Riemannian pseudomanifolds, Proc. Symp. Pure Math., AMS Providence R.I., XXXVI (1980), 91-146. | Zbl | MR
[Che3] , Spectral geometry of singular Riemannian spaces, J. Diff. Geom., 18-4 (1983), 575-657. | Zbl | MR
[Gro1] , Paul Levy's isoperimetric inequality (1980) Preprint, IHES.
[Gro2] , Dimension, non-linear spectra and width, Springer Lecture Notes, 1317 (1988), 132-185. | Zbl | MR
[Gro3] , Entropy, homology and semialgebraic geometry (after Yomdin), Astérisque, Soc. Math. France, 145-146 (1987), 225-241. | Zbl | MR | Numdam
[Gro4] , Curvature, diameter and Betti numbers, Comm. Math. Helv., 56 (1981), 179-195. | Zbl | MR
[Kho] , Fewnomials, Translation of Math. Monographs, V. 88, AMS, 1991. | Zbl
[Mil] , On the Betti numbers of real varieties, Proc. Am. Math. Soc., 15 (1964), 275-280. | Zbl | MR
[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
[Yom] , Global bounds for the Betti numbers of regular fibers of differential mappings, Topology, 24-2 (1985), 145-152. | Zbl | MR
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