On Strongly Pseudo-convex Kähler Manifolds.
On symmetry of the pluricomplex Green function for ellipsoids
We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.
On the Bergman distance on model domains in ℂⁿ
Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in and let D denote the “model domain” z ∈ ℂⁿ | r(z):= Re z₁ + P(z’) < 0. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.
On the embedding and compactification of -complete manifolds
We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as where is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into .
On the embedding of 1-convex manifolds with 1-dimensional exceptional sets.
On the embedding of 1-convex manifolds with 1-dimensional exceptional set
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold , with 1- dimensional exceptional set and finitely generated second homology group , is embeddable in if and only if is Kähler, and this case occurs only when does not contain any effective curve which is a boundary.
On the Geodesics of the Bergman Metric.
On the Geometry of Moduli Spaces.
On the Green function on a certain class of hyperconvex domains
We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain D that admits a smooth plurisubharmonic exhaustion function ψ such that 1/|ψ| is integrable near the boundary of D, and moreover satisfies the estimate at points close enough to the boundary with constants C,C’ > 0 and 0 < α < 1. Furthermore, we obtain a Hopf lemma for such a function ψ. Finally, we prove a lower bound on the Bergman distance on D.
On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics
On the homology groups of -complete spaces
On the Kähler form of the moduli space of once punctured tori.
On the Kählerian geometry of 1-convex threefolds.
On the Kobayashi and Caratheodory pseudometric reductions of homogeneous complex spaces
On the Kobayashi metric for perturbations of the ball.
On the Kobayashi-Royden metric for ellipsoids.
On the product property of the Carathéodory pseudodistance
We prove that, for certain domains , continuous product of domains , the Carathéodory pseudodistance satisfies the following product property
On the spectral Nevanlinna-Pick problem
We give several characterizations of the symmetrized n-disc Gₙ which generalize to the case n ≥ 3 the characterizations of the symmetrized bidisc that were used in order to solve the two-point spectral Nevanlinna-Pick problem in ℳ ₂(ℂ). Using these characterizations of the symmetrized n-disc, which give necessary and sufficient conditions for an element to belong to Gₙ, we obtain necessary conditions of interpolation for the general spectral Nevanlinna-Pick problem. They also allow us to give a...
On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball
Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a “generalized” tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.
On two conjectures of Hartshorne's.