Some extremal problems in conformal and quasiconformal 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...
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Conformal maps are widely used in geometry processing applications. They are smooth, preserve angles, and are locally injective by construction. However, conformal maps do not allow for boundary positions to be prescribed. A natural extension to the space of conformal maps is the richer space of quasiconformal maps of bounded conformal distortion. Extremal quasiconformal maps, that is, maps min...
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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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is achieved. This is given by e¡ = (1 -\-'Kkj)~1hj, where X is the unique positive root of £"-0 kj(l +\k])-1\hj\2 = M2. Davis proved the result by first considering the extremal problem for ra dimensional Euclidean space Rn. In this case the problem has the following geometric interpretation : (a") Let E be the hyperellipse {(oi, • • • , an): ]£?„„ kjOJ^M2} in Rn and suppose that h = (hi, • ■ ■...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1980
ISSN: 0026-2285
DOI: 10.1307/mmj/1029002313