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Diastatic entropy and rigidity of complex hyperbolic manifolds

Roberto Mossa (2016)

Complex Manifolds

Let f : Y → X be a continuous map between a compact real analytic Kähler manifold (Y, g) and a compact complex hyperbolic manifold (X, g0). In this paper we give a lower bound of the diastatic entropy of (Y, g) in terms of the diastatic entropy of (X, g0) and the degree of f . When the lower bound is attained we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G. Courtois and S. Gallot [2] for the volume entropy. As a corollary,when X = Y,we...

Embedding subsets of tori Properly into ℂ 2

Erlend Fornæss Wold (2007)

Annales de l’institut Fourier

Let 𝕋 be a complex one-dimensional torus. We prove that all subsets of 𝕋 with finitely many boundary components (none of them being points) embed properly into ℂ 2 . We also show that the algebras of analytic functions on certain countably connected subsets of closed Riemann surfaces are doubly generated.

Étude des jets de Demailly-Semple en dimension 3

Erwan Rousseau (2006)

Annales de l’institut Fourier

Dans cet article nous faisons l’étude algébrique des jets de Demailly-Semple en dimension 3 en utilisant la théorie des invariants des groupes non réductifs. Cette étude fournit la caractérisation géométrique du fibré des jets d’ordre 3 sur une variété de dimension 3 et permet d’effectuer, par Riemann-Roch, un calcul de caractéristique d’Euler.

Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric

Ngaiming Mok (2012)

Journal of the European Mathematical Society

We study the extension problem for germs of holomorphic isometries f : ( D ; x 0 ) → ( Ω ; f ( x 0 ) ) up to normalizing constants between bounded domains in Euclidean spaces equipped with Bergman metrics d s D 2 on D and d s Ω 2 on Ω . Our main focus is on boundary extension for pairs of bounded domains ( D , Ω ) such that the Bergman kernel K D ( z , w ) extends meromorphically in ( z , w ¯ ) to a neighborhood of D ¯ × D , and such that the analogous statement holds true for the Bergman kernel K Ω ( ς , ξ ) on Ω . Assuming that ( D ; d s D 2 ) and ( Ω ; d s Ω 2 ) are complete Kähler manifolds, we prove that the germ...

Extension of holomorphic bundles to the disc (and Serre’s Problem on Stein bundles)

Jean-Pierre Rosay (2007)

Annales de l’institut Fourier

Holomorphic bundles, with fiber ℂ n , defined on open sets in ℂ by locally constant transition automorphisms, are shown to extend to holomorphic bundles on the Riemann sphere. In particular, it allows us to give an example of a non-Stein holomorphic bundle on the unit disc, with polynomial transition automorphisms.

Extremal Kähler metrics on blow-ups of parabolic ruled surfaces

Carl Tipler (2013)

Bulletin de la Société Mathématique de France

New examples of extremal Kähler metrics are given on blow-ups of parabolic ruled surfaces. The method used is based on the gluing construction of Arezzo, Pacard and Singer [5]. This enables to endow ruled surfaces of the form ( 𝒪 ⊕ L ) with special parabolic structures such that the associated iterated blow-up admits an extremal metric of non-constant scalar curvature.

Currently displaying 101 – 120 of 403