Some Problems in Conformal Mapping
نویسندگان
چکیده
منابع مشابه
Remarks on "some Problems in Conformal Mapping"
1. The present note contains several remarks on an earlier paper by the author [2].1 In Chapter IV, §4, which deals with the question of when we can have equality of modules for a triply-connected domain and a proper subdomain, the last sentence was added in proof. This accounts for the apparent disparity between it and the preceding one. In order to justify this statement we observe first that...
متن کاملAnother Remark on "some Problems in Conformal Mapping"
In a great many cases the methods used in the proofs of the above theorems can be used to determine whether a given continuum is a Wn set. In particular, they can be used to prove that no W-¡ set, M, has a complementary domain whose boundary, /, contains three limit points of B(M) — J, no Wi set has a complementary domain whose boundary contains five such points, and that there exists a Wo set ...
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Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection–diffusion equations for potential flows, and...
متن کاملA General Class of Problems in Conformal Mapping.
belongs to class S if f(z) is regular and schlicht in zI < 1 and a, = 1. Let R be a closed set lying in zj < 1, and let *,1,(r) be a measure function defined in the space R. Given an integer n there is a number M M. such that If()-(z) < M for all z C R and for v = O, 1, 2, ..., n when f(z) belongs to class S. Let F,(ro Ro, ..., rny ) denote a complex-valued function which is continuous together...
متن کاملSome Inequalities Relating to Conformal Mapping upon Canonical Slit-domains
(1) f = se(z) = z + — + • • • z and which maps D conformally and bi-uniformly upon a domain De of the f-plane bounded by n rectilinear slits each of which makes the angle 0 with the positive direction of the real axis. The domain De is itself also uniquely determined for each value of 0. In the present paper we shall derive two inequalities involving the coefficient a$ appearing in (1) and the ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1949
ISSN: 0002-9947
DOI: 10.2307/1990479