Generation of the Ahlfors Five Islands Theorem
نویسنده
چکیده مقاله:
این مقاله چکیده ندارد
منابع مشابه
NEW PROOF OF THE AHLFORS FIVE ISLANDS THEOREM 339 from
Let D j, j = 1 , . . . , 5, be simply-connected domains on the Riemann sphere with piecewise analytic boundary and pairwise disjoint closures. Let D C C be a domain and denote by 3rA(D) = f a (D, {Dj}~=I) the family of all meromorphic functions f : D ~ C with the property that no subdomain of D is mapped conformally onto one of the domains Dj by f . (If there is such a subdomain, then it is cal...
متن کاملThe Role of the Ahlfors Five Islands Theorem in Complex Dynamics
The Ahlfors five islands theorem has become an important tool in complex dynamics. We discuss its role there, describing how it can be used to deal with a variety of problems. This includes questions concerning the Hausdorff dimension of Julia sets, the existence of singleton components of Julia sets, and the existence of repelling periodic points. We point out that for many applications a simp...
متن کاملAn Ahlfors Islands Theorem for Non-archimedean Meromorphic Functions
We present a p-adic and non-archimedean version of Ahlfors’ Five Islands Theorem for meromorphic functions, extending an earlier theorem of the author for holomorphic functions. In the non-archimedean setting, the theorem requires only four islands, with explicit constants. We present examples to show that the constants are sharp and that other hypotheses of the theorem cannot be removed.
متن کاملOn the Ahlfors Finiteness Theorem
The goal of this note is to give a proof of the Ahlfors Finiteness theorem which requires just the bare minimum of the complex analysis: (a) the existence theorem for the Beltrami equation and (b) the Rado-Cartan uniqueness theorem for holomorphic functions. However our proof does require some (by now standard) 3-dimensional topology and Greenberg's algebraic trick to deal with the triply-punct...
متن کاملA Theorem of Ahlfors for Hyperbolic Spaces
L. Ahlfors has proved that if the Dirichlet fundamental polyhedron of a Kleinian group G in the unit ball B3 has finitely many sides, then the normalized Lebesgue measure of L(G) is either zero or one. We generalize this theorem and a theorem of Beardon and Maskit to the n-dimensional case.
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 36 شماره No. 1
صفحات 175- 182
تاریخ انتشار 2011-01-23
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023