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Mesures de Mahler et équidistribution logarithmique

Antoine Chambert-Loir, Amaury Thuillier (2009)

Annales de l’institut Fourier

Soit X un schéma projectif intègre défini sur un corps de nombres  F  ; soit L un fibré en droites ample sur  X muni d’une métrique adélique semi-positive au sens de Zhang. Les résultats principaux de cet article sont :(1)Une formule qui calcule les hauteurs locales (relativement à  L ) d’un diviseur de Cartier sur  X comme des « mesures de Mahler » généralisées, c’est-à-dire les intégrales de fonctions de Green pour  D contre des mesures associées à  L  ;(2)Un théorème d’équidistribution des points de « petite »...

Metrics with homogeneous geodesics on flag manifolds

Dimitri V. Alekseevsky, Andreas Arvanitoyeorgos (2002)

Commentationes Mathematicae Universitatis Carolinae

A geodesic of a homogeneous Riemannian manifold ( M = G / K , g ) is called homogeneous if it is an orbit of an one-parameter subgroup of G . In the case when M = G / H is a naturally reductive space, that is the G -invariant metric g is defined by some non degenerate biinvariant symmetric bilinear form B , all geodesics of M are homogeneous. We consider the case when M = G / K is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group G , and we give a simple necessary condition that M admits a non-naturally reductive...

Michael's theorem for Lipschitz cells in o-minimal structures

Małgorzata Czapla, Wiesław Pawłucki (2016)

Annales Polonici Mathematici

A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.

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