Spectral geometry of semi-algebraic sets
Annales de l'Institut Fourier, …, Tome 42 (1992) no. 1-2, pp. 249-274.

Nous étudions le spectre de l’opérateur de Laplace sur les ensembles algébriques et semi-algébriques dans R N .

The spectrum of the Laplace operator on algebraic and semialgebraic subsets A in R N is studied and the number of small eigenvalues is estimated by the degree of A.

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     title = {Spectral geometry of semi-algebraic sets},
     journal = {Annales de l'Institut Fourier},
     pages = {249--274},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {42},
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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. http://www.numdam.org/articles/10.5802/aif.1291/

[At] M. Atiyah, Resolution of singularities and division of distributions, Comm. Pure Appl. Math., 23 (1970), 145-150. | MR | Zbl

[Ber] I. Bernstein, Moduli over the ring of differential operators, Funct. Anal. and App.

[BerGel] I. Bernstein, S. Gelfand, Meromorphicity of the function pλ, Funct. Anal and Applic., (Russian), 3-1 (1969), 84-85.

[Bj] J. Björk, Rings of differential operators, North-Holland Publ. Co. Math. Libr., 21 (1979). | MR | Zbl

[Che1] J. Cheeger, 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 | Zbl

[Che2] J. Cheeger, On the Hodge theory of Riemannian pseudomanifolds, Proc. Symp. Pure Math., AMS Providence R.I., XXXVI (1980), 91-146. | MR | Zbl

[Che3] J. Cheeger, Spectral geometry of singular Riemannian spaces, J. Diff. Geom., 18-4 (1983), 575-657. | MR | Zbl

[Gro1] M. Gromov, Paul Levy's isoperimetric inequality (1980) Preprint, IHES.

[Gro2] M. Gromov, Dimension, non-linear spectra and width, Springer Lecture Notes, 1317 (1988), 132-185. | MR | Zbl

[Gro3] M. Gromov, Entropy, homology and semialgebraic geometry (after Yomdin), Astérisque, Soc. Math. France, 145-146 (1987), 225-241. | Numdam | MR | Zbl

[Gro4] M. Gromov, Curvature, diameter and Betti numbers, Comm. Math. Helv., 56 (1981), 179-195. | MR | Zbl

[Kho] A.G. Khovanskii, Fewnomials, Translation of Math. Monographs, V. 88, AMS, 1991. | Zbl

[Mil] J. Milnor, On the Betti numbers of real varieties, Proc. Am. Math. Soc., 15 (1964), 275-280. | MR | Zbl

[Tho] R. Thom, 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] Y. Yomdin, Global bounds for the Betti numbers of regular fibers of differential mappings, Topology, 24-2 (1985), 145-152. | MR | Zbl

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