Spectral geometry of semi-algebraic sets

Mikhael Gromov

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 1-2, page 249-274
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Gromov, Mikhael. "Spectral geometry of semi-algebraic sets." Annales de l'institut Fourier 42.1-2 (1992): 249-274. <http://eudml.org/doc/74953>.

@article{Gromov1992,
abstract = {The spectrum of the Laplace operator on algebraic and semialgebraic subsets $A$ in $\{\bf R\}^N$ is studied and the number of small eigenvalues is estimated by the degree of $A$.},
author = {Gromov, Mikhael},
journal = {Annales de l'institut Fourier},
keywords = {algebraic set; singularities; semianalytic set; Laplace operator; eigenvalues; isoperimetric profile},
language = {eng},
number = {1-2},
pages = {249-274},
publisher = {Association des Annales de l'Institut Fourier},
title = {Spectral geometry of semi-algebraic sets},
url = {http://eudml.org/doc/74953},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Gromov, Mikhael
TI - Spectral geometry of semi-algebraic sets
JO - Annales de l'institut Fourier
PY - 1992
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 1-2
SP - 249
EP - 274
AB - The spectrum of the Laplace operator on algebraic and semialgebraic subsets $A$ in ${\bf R}^N$ is studied and the number of small eigenvalues is estimated by the degree of $A$.
LA - eng
KW - algebraic set; singularities; semianalytic set; Laplace operator; eigenvalues; isoperimetric profile
UR - http://eudml.org/doc/74953
ER -

References

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  5. [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. Zbl0212.44903MR53 #6645
  6. [Che2] J. CHEEGER, On the Hodge theory of Riemannian pseudomanifolds, Proc. Symp. Pure Math., AMS Providence R.I., XXXVI (1980), 91-146. Zbl0461.58002MR83a:58081
  7. [Che3] J. CHEEGER, Spectral geometry of singular Riemannian spaces, J. Diff. Geom., 18-4 (1983), 575-657. Zbl0529.58034MR85d:58083
  8. [Gro1] M. GROMOV, Paul Levy's isoperimetric inequality (1980) Preprint, IHES. 
  9. [Gro2] M. GROMOV, Dimension, non-linear spectra and width, Springer Lecture Notes, 1317 (1988), 132-185. Zbl0664.41019MR90d:58022
  10. [Gro3] M. GROMOV, Entropy, homology and semialgebraic geometry (after Yomdin), Astérisque, Soc. Math. France, 145-146 (1987), 225-241. Zbl0611.58041MR89f:58082
  11. [Gro4] M. GROMOV, Curvature, diameter and Betti numbers, Comm. Math. Helv., 56 (1981), 179-195. Zbl0467.53021MR82k:53062
  12. [Kho] A.G. KHOVANSKII, Fewnomials, Translation of Math. Monographs, V. 88, AMS, 1991. Zbl0728.12002
  13. [Mil] J. MILNOR, On the Betti numbers of real varieties, Proc. Am. Math. Soc., 15 (1964), 275-280. Zbl0123.38302MR28 #4547
  14. [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. Zbl0137.42503
  15. [Yom] Y. YOMDIN, Global bounds for the Betti numbers of regular fibers of differential mappings, Topology, 24-2 (1985), 145-152. Zbl0566.57014MR87a:58030

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