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We derive conditions under which a holomorphic mapping of a taut Riemann surface must be an automorphism. This is an analogue involving invariant distances of a result of H. Cartan. Using similar methods we prove an existence result for 1-dimensional holomorphic retracts in a taut complex manifold.
Let be a holomorphic Banach bundle over a compact complex manifold, which can be defined by a cocycle of holomorphic transition functions with values of the form where is compact. Assume that the characteristic fiber of has the compact approximation property. Let be the complex dimension of and . Then: If is a holomorphic vector bundle (of finite rank) with , then . In particular, if , then .
We introduce a new invariant Kähler metric on relatively compact domains in a complex manifold, which is the Bergman metric of the L² space of holomorphic sections of the pluricanonical bundle equipped with the Hermitian metric introduced by Narasimhan-Simha.
We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.
We show a relation between the Kobayashi pseudodistance of a holomorphic fiber bundle and the Kobayashi pseudodistance of its base. Moreover, we prove that a holomorphic fiber bundle is taut iff both the fiber and the base are taut.
Let an open set in near , a suitable holomorphic function near . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : , ( is a form, closed in in with supp, then we deduce an extension result for functions on , as holomorphic fonctions in .
Let be the open unit ball of a Banach space , and let be a holomorphic map with . In this paper, we discuss a condition whereby is a linear isometry on .
Soit un groupe de Lie complexe et une forme réelle fermée de . Un couple est dit pseudo-convexe, s’il existe sur une fonction régulière, strictement p.s.h., invariante par l’action de et d’exhaustion sur . On dit que est à spectre imaginaire pur, si pour tout de Lie, les valeurs propres de ad sont imaginaires pures. Pour à radical simplement connexe, cette dernière propriété équivaut à la pseudo-convexité de . Pour pseudo-convexe et sous une hypothèse de sous-groupe discret,...
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