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Conditions de Bohr-Sommerfeld pour les singularités focus-focus et monodromie quantique

San Vũ Ngọc (1998)

Journées équations aux dérivées partielles

Je présenterai les résultats d’une étude microlocale détaillée du spectre joint de deux opérateurs h-pseudo-différentiels qui commutent sur une variété de dimension deux en présence d’une singularité dite «focus-focus». L’étude couvre par exemple le cas du pendule sphérique étudié par Duistermaat, ou du fond de la bouteille de champagne, mais les phénomènes observés sont universels. On en observe principalement deux: une accumulation de valeurs propres au voisinage de la singularité en O ( l o g ( h ) ) par rapport...

Cône normal et régularités de Kuo-Verdier

Patrice Orro, David Trotman (2002)

Bulletin de la Société Mathématique de France

Nous introduisons de nouvelles régularités de Kuo-Verdier ( r e ) et montrons que pour une stratification C 2 ( a + r e ) ...

Conformal curvature for the normal bundle of a conformal foliation

Angel Montesinos (1982)

Annales de l'institut Fourier

It is proved that the normal bundle of a distribution 𝒱 on a riemannian manifold admits a conformal curvature C if and only if 𝒱 is a conformal foliation. Then is conformally flat if and only if C vanishes. Also, the Pontrjagin classes of can be expressed in terms of C .

Conformal Geometry and the Composite Membrane Problem

Sagun Chanillo (2013)

Analysis and Geometry in Metric Spaces

We show that a certain eigenvalue minimization problem in two dimensions for the Laplace operator in conformal classes is equivalent to the composite membrane problem. We again establish such a link in higher dimensions for eigenvalue problems stemming from the critical GJMS operators. New free boundary problems of unstable type arise in higher dimensions linked to the critical GJMS operator. In dimension four, the critical GJMS operator is exactly the Paneitz operator.

Conformal gradient vector fields on a compact Riemannian manifold

Sharief Deshmukh, Falleh Al-Solamy (2008)

Colloquium Mathematicae

It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying 0 < Ric ≤ (n-1)(2-nc/λ₁)c for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold forces it to...

Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity

Erwann Aubry, Colin Guillarmou (2011)

Journal of the European Mathematical Society

For odd-dimensional Poincaré–Einstein manifolds ( X n + 1 , g ) , we study the set of harmonic k -forms (for k < n / 2 ) which are C m (with m ) on the conformal compactification X ¯ of X . This set is infinite-dimensional for small m but it becomes finite-dimensional if m is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology H k ( X ¯ , X ¯ ) and the kernel of the Branson–Gover [3] differential operators ( L k , G k ) on the conformal infinity ( X ¯ , [ h 0 ] ) . We also relate the set of C n - 2 k + 1 ( Λ k ( X ¯ ) ) forms in the kernel of d + δ g to the conformal...

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