Hankel Operators on Bergman Spaces with Change of Weight.
Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
We give here a generalization of the theory of optimal destabilizing 1-parameter subgroups to non algebraic complex geometry : we consider holomorphic actions of a complex reductive Lie group on a finite dimensional (possibly non compact) Kähler manifold. In a second part we show how these results may extend in the gauge theoretical framework and we discuss the relation between the Harder-Narasimhan filtration and the optimal detstabilizing vectors of a non semistable object....
Hardy spaces and analytic continuation of Bergman spaces
Hardy spaces of analytic multifunctions.
Hardy spaces on two-sheeted covering semigroups.
Harmonic and analytic functions admitting a distribution boundary value
Harmonic Bergman kernel for some balls.
Harmonic diffeomorphisms and Teichmüller theory.
Harmonic functions on classical rank one balls
In questo articolo studieremo le relazioni fra le funzioni armoniche nella palla iperbolica (sia essa reale, complessa o quaternionica), le funzione armoniche euclidee in questa palla, e le funzione pluriarmoniche sotto certe condizioni di crescita. In particolare, estenderemo al caso quaternionico risultati anteriori dell'autore (nel caso reale), e di A. Bonami, J. Bruna e S. Grellier (nel caso complesso).
Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces H... and N*.
Harmonic maps and representations of non-uniform lattices of
We study representations of lattices of into . We show that if a representation is reductive and if is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic -space to complex hyperbolic -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into of non-uniform lattices in , and more generally of fundamental groups of orientable...
Harmonic Maps of the Moduli Space of Compact Riemann Surfaces.
Harmonic metrics and connections with irregular singularities
We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface with the complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same complex.
Harmonie Forms Dual to Geodesic Cycles in Quotients of SU (p, 1).
Harmonie Mappings and Kähler Manifolds.
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term.
Hartogs extension phenomena for analytic curves.
Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring
In this paper we prove that the projective dimension of is , where is the ring of polynomials in variables with complex coefficients, and is the module generated by the columns of a matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of quaternionic variables. As a corollary we show that the sheaf of regular functions has flabby dimension , and we prove a cohomology vanishing theorem for open...
Hartogs theorem for forms : solvability of Cauchy-Riemann operator at critical degree
The Hartogs Theorem for holomorphic functions is generalized in two settings: a CR version (Theorem 1.2) and a corresponding theorem based on it for -closed forms at the critical degree, (Theorem 1.1). Part of Frenkel’s lemma in category is also...
Hartogs type extension theorems on some domains in Kähler manifolds
Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact Kähler and...