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Extending algebraic actions.

Arthur G. Wasserman (1999)

Revista Matemática Complutense

There is a well-known procedure -induction- for extending an action of a subgroup H of a Lie group G on a topological space X to an action of G on an associated space. Induction can also extend a smooth action of a subgroup H of a Lie group G on a manifold M to a smooth action of G on an associated manifold. In this paper elementary methods are used to show that induction also works in the category of (nonsingular) real algebraic varieties and regular or entire maps if G is a compact abelian Lie...

Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X be a complex manifold, S a generic submanifold of X R , the real underlying manifold to X . Let Ω be an open subset of S with ∂ ⁡ Ω analytic, Y a complexification of S . We first recall the notion of Ω -tuboid of X and of Y and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ∂ ¯ b to the extendability of C ⁢ R functions on Ω to Ω -tuboids of X . Next, if X has complex dimension 2, we give results on extension...

Extension of smooth functions in infinite dimensions II: manifolds

C. J. Atkin (2002)

Studia Mathematica

Let M be a separable C ∞ Finsler manifold of infinite dimension. Then it is proved, amongst other results, that under suitable conditions of local extensibility the germ of a C ∞ function, or of a C ∞ section of a vector bundle, on the union of a closed submanifold and a closed locally compact set in M, extends to a C ∞ function on the whole of M.

Extrema de valeurs propres dans une classe conforme

Pierre Jammes (2005/2006)

Séminaire de théorie spectrale et géométrie

On s’intéresse au problème de savoir quelle est la rigidité apportée au spectre d’une variété riemannienne compacte par le fait de fixer son volume et se classe conforme, et en particulier de déterminer si on peut faire tendre les valeurs propres vers 0 ou l’infini sous cette contrainte. On considère successivement les cas du laplacien usuel agissant sur les fonctions, l’opérateur de Dirac, le laplacien conforme et le laplacien de Hodge-de Rham.

Extremal domains for the first eigenvalue of the Laplace-Beltrami operator

Frank Pacard, Pieralberto Sicbaldi (2009)

Annales de l’institut Fourier

We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Riemannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.

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