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Homogeneous bundles and the first eigenvalue of symmetric spaces

Leonardo Biliotti, Alessandro Ghigi (2008)

Annales de l’institut Fourier

In this note we prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kähler metric on a compact Hermitian symmetric spaces of ABCD–type.

Homogeneous extremal function for a ball in ℝ²

Mirosław Baran (1999)

Annales Polonici Mathematici

We point out relations between Siciak’s homogeneous extremal function Ψ B and the Cauchy-Poisson transform in case B is a ball in ℝ². In particular, we find effective formulas for Ψ B for an important class of balls. These formulas imply that, in general, Ψ B is not a norm in ℂ².

Homogeneous polynomials with isomorphic Milnor algebras

Imran Ahmed (2010)

Czechoslovak Mathematical Journal

We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.

Homologie des ensembles semi-pfaffiens

Jean-Marie Lion, Jean-Philippe Rolin (1996)

Annales de l'institut Fourier

Un sous-ensemble pfaffien d’un ouvert semi-analytique M R n est une intersection finie d’ensembles semi-analytiques relativement compacts de R n et de feuilles non spiralantes de certains feuilletages analytiques de codimension 1 de M . Les sous-ensembles semi-pfaffiens de M sont les éléments de la plus petite classe de sous-ensembles de M contenant les sous-ensembles pfaffiens de M , stable par intersection finie, réunion finie et différence symétrique. Les ensembles T -pfaffiens sont les éléments de la...

Homology for irregular connections

Spencer Bloch, Hélène Esnault (2004)

Journal de Théorie des Nombres de Bordeaux

Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration defines a perfect pairing between de Rham cohomology with values in the connection and homology with values in the dual connection.

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