2 edition of **Quasirational mappings on parabolic Riemann surfaces.** found in the catalog.

Quasirational mappings on parabolic Riemann surfaces.

Ilpo Laine

- 207 Want to read
- 23 Currently reading

Published
**1970**
by Suomalainen Tiedeakatemia in Helsinki
.

Written in English

- Riemann surfaces.,
- Analytic mappings.

**Edition Notes**

Bibliography: p. [26]

Series | Annales Academiae Scientiarum Fennicae. Series A. I: Mathematica 482 |

Classifications | |
---|---|

LC Classifications | Q60 .H5232 no. 482, QA333 .H5232 no. 482 |

The Physical Object | |

Pagination | 25, [1] p. |

Number of Pages | 25 |

ID Numbers | |

Open Library | OL5174206M |

LC Control Number | 74878635 |

Book Description: This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This . The complement of a Cantor set in the complex plane is itself regarded as a Riemann surface of infinite type. The problem is the quasiconformal equivalence of such Riemann : Hiroshige Shiga.

It is ultimately shown (Theorem ) that a marked Riemann surface on which there is an exhaustion function with bounded charge satis es our criterion. Let be a measureable one form on the Riemann surface X. Suppose z= x1+ix2 is a coordinate on UˆX and write U = f1dx1 + f2dx2 Now set U = f2dx1 + f1dx2 We can use the Cauchy-Riemann File Size: 1MB. This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and Cited by:

In terms of Riemann surfaces, the Riemann mapping theorem can be formulated as follows: Any simply-connected Riemann surface is conformally equivalent to one of the following three domains: 1) the extended complex plane, i.e. the Riemann sphere (the elliptic case); 2) the finite complex plane, i.e. the punctured Riemann sphere (the parabolic. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. that an analytic map from a parabolic Riemann surface to a hyperbolic Riemann surface .

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Quasiconformal mappings and Riemann surfaces Add library to Favorites Please choose whether or not you want other users to be able to see on your profile that this library is a favorite of yours.

Abstract. In I to 12 we encountered examples of R p-surfaces, i.e., surfaces possessing capacity functions with compact level shall now draw such surfaces under a more systematic study and show that every parabolic surface Author: Leo Sario, Kiyoshi Noshiro.

There is a part in the book which I don't understand and I would like to ask for books and references Stack Exchange Network Stack Exchange network consists of Q&A communities including Stack.

It is gratifying to learn that there is new life in an old field that has been at the center of one's existence for over a quarter of a century. It is particularly pleasing that the subject of Riemann surfaces has 5/5(1). Parabolic Curves Tangent to Holomorphic Foliations 30 Nevanlinna’s Currents Associated to a Parabolic Riemann Surface 30 Metrics on the tangent bundle of a holomorphic foliation by disks 33 Degree of currents associated to parabolic Riemann surfaces File Size: KB.

] ON SEMI-PARABOLIC RIEMANN SURFACES If W is a bordered surface we will call a collection {Q„} of connected finite subsurfaces an exhaustion of W if Sln — Q.'„ n W, where Quasirational mappings on parabolic Riemann surfaces.

book is an. fr,po LlrNn, Quasirational mappings. on parabolic Riemann. surfaces. A region. on a. Riemann surface -B. said. be regular, if. is compact, if. The potential theory proof of the Riemann mapping theorem 3. Existence of Green functions via Perron’s method 4.

Behavior at the boundary Chapter Green functions and the classiﬁcation problem 1. Green functions on Riemann surfaces 2. Hyperbolic Riemann surfaces File Size: 1MB.

functions for the Laplace operator on Riemann surfaces. The Green function on a Riemann surface is an integral kernel which solves the Poisson equation 2i∂∂f¯ = φ.

More precisely, let Xbe a compact connected Riemann surface. HARMONIC FUNCTIONS ON OPEN RIEMANN SURFACES 41 linna, or if it does not have a Green's function, then it is parabolic. We also give a criterion in terms of the continuous linear functionals on the space BD that a Riemann surface.

This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. This subject is large and. Parabolic Riemann surfaces could be hyperbolic in the Kobayashi sense, i.e admit a Poincaré metric.

Let X be a manifold of general type, and let A be an ample line bundle on X. Hyperbolic geometry of Riemann surfaces By Theoremall hyperbolic Riemann surfaces inherit the geometry of the hyperbolic plane.

How this geometry interacts with the topology of a Riemann surface is a complicated business, and beginning with Sectionthe material will become more demanding.

Since this book. 10 CHAPTER 1. HOLOMORPHIC FUNCTIONS The second integral is deﬁned for all z, and holomorphic in z. We write the ﬁrst integral as Z1 0 tz−1(et−1)dt+ Z1 0 tz−1dt. Now the term Z 1. Publisher Summary. This chapter discusses the functions y = f (x), x = (x 1, x 2, x n), y = (y 1, y 2, y n) defining mappings of regions of n space R n, n ≥ f is a local homeomorphism and defines a Q-quasiconformal mapping.

Introduction to Compact Riemann Surfaces Alexander I. Bobenko Institut fu¨r Mathematik, Technische Universit¨at Berlin, Strasse des Juni, Berlin, Germany, [email protected] The theory of Riemann. Broadly speaking the division of the book is as follows: The Introduction and Chapters I to III deal mainly with the theory of mappings of arbitrary Riemann surfaces as developed by the first named author; Chapter IV, due to Nakai, is devoted to meromorphic functions on parabolic surfaces.

This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmüller Spaces, held in honor of Clifford J. Earle, from. ALGEBRAIC GEOMETRY AND RIEMANN SURFACES DANIEL YING Abstract.

In this thesis we will give a present survey of the various methods used in dealing with Riemann surfaces. Riemann surfaces are central in mathematics because of the multiple If X and Y are topological spaces (surfaces), a covering map is a continuous mapping File Size: KB.

Samuel L. Krushkal, in Handbook of Complex Analysis, Teichmüller’s theory of extremal quasiconformal maps. In Teichmüller gave an extremely fruitful extension of the Grötzsch problem to the maps of Riemann surfaces of finite analytic type.

Recall that a Riemann surface X is a connected one-dimensional complex manifold, i.e., a topological surface.

This may be viewed as a generalisation of the Riemann Mapping Theorem, which states that any (connected, simply-connected, proper) open subset of the complex plane is conformally equivalent to the unit disk. Note that a Riemann surface is an orientable 2-manifold, and conversely any orientable 2-manifold can be given a Riemann surface .If a domain on a Riemann surface has a component of the frontier with at least two distinct points then it is potential theoretic hyperbolic.

This result goes back to Osgood. Existence of green 's function is .