منابع مشابه
Hyperbolicity in Unbounded Convex Domains
We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.
متن کاملGromov hyperbolicity and the Kobayashi metric
It is well known that the unit ball endowed with the Kobayashi metric is isometric to complex hyperbolic space and in particular is an example of a negatively curved Riemannian manifold. One would then suspect that when Ω ⊂Cd is a domain close to the unit ball then (Ω ,KΩ ) should be negatively curved (in some sense). Unfortunately, for general domains the Kobayashi metric is no longer Riemanni...
متن کاملThe Arithmetic and the Geometry of Kobayashi Hyperbolicity
(1) The dimension of the pluricanonical series, h(C,mK), grows linearly with m for curves of genus at least two. (2) The canonical/cotangent bundle of a curve of genus at least two is ample. (3) A curve of genus at least two admits a hyperbolic metric with constant negative curvature. (4) Curves of genus at least two are uniformized by the unit disc, hence they do not admit any non-constant hol...
متن کاملDomains Which Are Locally Uniformly Linearly Convex in the Kobayashi Distance
Recently, in [1], it has been proved that if B is an open unit ball in a Cartesian product l2 × l2 furnished with the lp-norm ‖ · ‖ and kB is the Kobayashi distance on B, then the metric space (B,kB) is locally uniformly convex in linear sense. Our construction of domains, which are locally uniformly convex in their Kobayashi distances, is based on the ideas from [1]. Such domains play an impor...
متن کاملApplication of computational invariant theory to Kobayashi hyperbolicity and to Green-Griffiths algebraic degeneracy
A major unsolved problem (according to Demailly 1997) towards the Kobayashi hyperbolicity conjecture in optimal degree is to understand jet differentials of germs of holomorphic discs that are invariant under any reparametrization of the source. The underlying group action is not reductive, but we provide a complete algorithm to generate all invariants, in arbitrary dimension n and for jets of ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1980
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1980-0572300-3