Spectral geometry of semi-algebraic sets

Mikhael Gromov

Displaying similar documents to “Spectral geometry of semi-algebraic sets”

On the polynomial-like behaviour of certain algebraic functions

Charles Feffermann, Raghavan Narasimhan (1994)

Annales de l'institut Fourier

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Given integers $D > 0, n > 1, 0 < r < n$ and a constant $C > 0$ , consider the space of $r$ -tuples $\vec{P} = (P_{1} ... P_{r})$ of real polynomials in $n$ variables of degree $\leq D$ , whose coefficients are $\leq C$ in absolute value, and satisfying $\det {(\frac{\partial P_{i}}{\partial x_{i}} (0))}_{1 \leq i, j \leq r} = 1$ . We study the family ${f | V}$ of algebraic functions, where $f$ is a polynomial, and $V = {| x | \leq δ, \vec{P} (x) = 0}, δ > 0$ being a constant depending only on $n, D, C$ . The main result is a quantitative extension theorem for these functions which is uniform in $\vec{P}$ . This is used to prove Bernstein-type inequalities which are again uniform with respect to $\vec{P}$ . ...

Bernstein's inequality on algebraic curves

Charles Fefferman, Raghavan Narasimhan (1993)

Annales de l'institut Fourier

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On the generic spectrum of a riemannian cover

Steven Zelditch (1990)

Annales de l'institut Fourier

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Let $M$ be a compact manifold let $G$ be a finite group acting freely on $M$ , and let $ℳ_{G}$ be the (Fréchet) space of $G$ -invariant metric on $M$ . A natural conjecture is that, for a generic metric in $ℳ_{G}$ , all eigenspaces of the Laplacian are irreducible (as orthogonal representations of $G$ ). In physics terminology, no “accidental degeneracies” occur generically. We will prove this conjecture when dim $M \geq$ dim $V$ for all irreducibles $V$ of $G$ . As an application, we construct isospectral manifolds with simple...

On the space of morphisms into generic real algebraic varieties

Riccardo Ghiloni (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We introduce a notion of generic real algebraic variety and we study the space of morphisms into these varieties. Let $Z$ be a real algebraic variety. We say that $Z$ is generic if there exist a finite family ${D_{i}}_{i = 1}^{n}$ of irreducible real algebraic curves with genus $\geq 2$ and a biregular embedding of $Z$ into the product variety $\prod_{i = 1}^{n} D_{i}$ . A bijective map $ϕ : {\tilde{Z}}^{} \to Z$ from a real algebraic variety $\tilde{Z}$ to $Z$ is called weak change of the algebraic structure of $Z$ if it is regular and its inverse is a Nash map. Generic real algebraic...

Thom's lemma in real geometry

I. Miranda, T. Recio (1988)

Banach Center Publications

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Semialgebraic and semianalytic sets

Jesus M. Ruiz (1991)

Cahiers du séminaire d'histoire des mathématiques

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