Extremal holomorphic curves for defect relations
نویسنده
چکیده
Drasin’s theorem describing meromorphic functions of finite order with maximal sum of deficiencies is extended to holomorphic curves in projective space. A conjecture about holomorphic curves extremal for Cartan’s defect relation is discussed.
منابع مشابه
Exterior Monge-Ampère Solutions
We discuss the Siciak-Zaharjuta extremal function of a real convex body in Cn, a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphic ...
متن کاملExterior Monge- Amp`ere Solutions
We discuss the Siciak-Zaharjuta extremal function of a real convex body in C n , a solution of the homogeneous complex Monge-Ampère equation on the exterior of the convex body. We determine several conditions under which a foliation by holomorphic curves can be found in the complement of the convex body along which the extremal function is harmonic. We study a variational problem for holomorphi...
متن کاملValue distribution and potential theory
We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard’s theorems to quasiregular maps between Riemannian manifolds, a version of the Second Main Theorem of Nevanlinna for curves in projective space and non-linear divisors, description of extremal function...
متن کاملLINEAR RELATIONS AMONG HOLOMORPHIC QUADRATIC DIFFERENTIALS AND INDUCED SIEGEL’S METRIC ON Mg MARCO MATONE AND ROBERTO VOLPATO
We derive the explicit form of the (g − 2)(g − 3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of canonical curves of genus g ≥ 4. It turns out that Petri’s relations remarkably match in determinantal conditions. We explicitly express the volume form on the moduli space M̂g of canonical curves induced by the Siegel metri...
متن کاملHolomorphic Curvature of Finsler Metrics and Complex Geodesics
If D is a bounded convex domain in C , then the work of Lempert [L] and Royden-Wong [RW] (see also [A]) show that given any point p ∈ D and any non-zero tangent vector v ∈ C at p, there exists a holomorphic map φ:U → D from the unit disk U ⊂ C into D passing through p and tangent to v in p which is an isometry with respect to the hyperbolic distance of U and the Kobayashi distance of D. Further...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999