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.
On values of homogeneous polynomials in discrete sets of points
Operator theory and the Carathéodory metric.