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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.

Homology of origamis with symmetries

Carlos Matheus, Jean-Christophe Yoccoz, David Zmiaikou (2014)

Annales de l’institut Fourier

Given an origami (square-tiled surface) M with automorphism group Γ , we compute the decomposition of the first homology group of M into isotypic Γ -submodules. Through the action of the affine group of M on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.

Hörmander systems and harmonic morphisms

Elisabetta Barletta (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a Hörmander system X = { X 1 , , X m } on a domain Ω 𝐑 n we show that any subelliptic harmonic morphism φ from Ω into a ν -dimensional riemannian manifold N is a (smooth) subelliptic harmonic map (in the sense of J. Jost & C-J. Xu, [9]). Also φ is a submersion provided that ν m and X has rank m . If Ω = 𝐇 n (the Heisenberg group) and X = 1 2 L α + L α ¯ , 1 2 i L α - L α ¯ , where L α ¯ = / z ¯ α - i z α / t is the Lewy operator, then a smooth map φ : Ω N is a subelliptic harmonic morphism if and only if φ π : ( C ( 𝐇 n ) , F θ 0 ) N is a harmonic morphism, where S 1 C ( 𝐇 n ) π 𝐇 n is the canonical circle bundle and F θ 0 is the Fefferman...

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