EUDML

We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then $H^{1} (G a m m a, Φ) \neq 0$ for some unitary representation $Φ$ . By our earlier work there exists a $d$ -closed holomorphic 1-form with coefficients twisted by some unitary representation $Φ^{'}$ , possibly non-isomorphic to $Φ$ . Taking norms we obtains a positive...

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 $f : (D; x_{0}) \to (Ω; f (x_{0}))$ 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 $(z, \bar{w})$ to a neighborhood of $\bar{D} \times D$ , 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...

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Rigidity of Holomorphic Self-Mappings and the Automorphism Groups of Hyperbolic Stein Spaces.

Uniqueness Theorems of Kähler Metrics of Semipositive Bisectional Curvature on Compact Hermitian Symetric Spaces.

The Serre Problem on Riemann Surfaces.

Complete Kähler-Einstein Metrics on Bounded Domains Locally of Finite Volume at Some Boundary Points.

The Holomorphic or Anti-Holomorphic Character of Harmonic Maps into Irreducible Compact Quotients of Polydiscs.

Steinness of universal covers of certain compact Kähler manifolds.

Factorization of semisimple discrete representations of Kähler groups.

Strong Rigidity of Irreducible Quotients of Polydiscs of Finite Volume.

An embedding theorem of complete Kähler manifolds of positive Ricci curvature onto quasi-projective varieties.

An embedding theorem of complete Kähler manifolds of positive bisectional curvature onto affine algebraic varieties

Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups

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

Rigidity of convex realizations of irreducible bounded symmetric domains of rank ...2.

Eigensections on Kuga families of abelian varieties and finiteness of their Mordell-Weil groups.

Uniruled projective manifolds with irreducible reductive G-structures.

Holomorphic immersions between compact hyperbolic space forms.

Deformation rigidity of the rational homogeneous space associated to a long simple root

The Poincaré-Lelong equation on complete Kähler manifolds