Spectral geometry of semi-algebraic sets. (English) Zbl 0759.58048

Gromov, Mikhael

Ann. Inst. Fourier 42, No. 1-2, 249-274 (1992).

The spectrum of the Laplace operator on algebraic and semialgebraic subsets \(A\) in \(\mathbb{R}^ N\) is studied and the number of small eigenvalues is estimated by the degree of \(A\).

Reviewer: M.Gromov (Bures-sur-Yvette)

MSC:

58J50	Spectral problems; spectral geometry; scattering theory on manifolds
14P10	Semialgebraic sets and related spaces
32B20	Semi-analytic sets, subanalytic sets, and generalizations

Keywords:

algebraic set; singularities; semianalytic set; Laplace operator; eigenvalues; isoperimetric profile

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