On an Extremal Metric Approach to Extremal Decomposition Problems

2017 ◽  
Vol 225 (6) ◽  
pp. 980-990
Author(s):  
G. V. Kuz’mina
Keyword(s):  
Extremal Decomposition ◽  
Extremal Metric

Extremal decomposition problems for p-harmonic Robin radius

2020 ◽  
Vol 20 (2) ◽  
pp. 135-143
Author(s):  
A.S. Afanaseva-Grigoreva ◽  
◽  
E.G. Prilepkina ◽  
Keyword(s):  
Euclidean Space ◽  
Extremal Decomposition ◽  
Families Of Curves

The theorems on the extremal decomposition of plane domains concerning to the products of Robin's radii are extended to the case of domains in Euclidean space. In some cases, the classical non-overlapping condition is weakened. The proofs are based on the moduli technique for families of curves and dissymmetrization.

scholarly journals On the Denjoy Conjecture

1958 ◽  
Vol 10 ◽  
pp. 627-631 ◽  
Author(s):  
James A. Jenkins
Keyword(s):  
Quasiconformal Mappings ◽  
Regular Functions ◽  
Extremal Metric

In recent years many of the properties of regular functions have been shown to extend to quasiconformal mappings. (The latter term is here understood in the sense defined in (5).) This is particularly true of those results which can be proved by use of the method of the extremal metric. It is rather strange, then, that a result which constitutes one of the first notable applications of this method has not been so extended (at least to the author's knowledge).

Extremal decomposition of the complex plane with free poles

2020 ◽  
Vol 246 (1) ◽  
pp. 1-17
Author(s):  
Aleksandr K. Bakhtin ◽  
Iryna V. Denega
Keyword(s):  
Complex Plane ◽  
Extremal Decomposition

Problem on extremal decomposition of the complex plane with free poles

2020 ◽  
Vol 17 (1) ◽  
pp. 3-29
Author(s):  
Aleksandr Bakhtin ◽  
Liudmyla Vyhivska
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Geometric Theory ◽  
Extremal Decomposition ◽  
Overlapping Domains

We consider the well-known problem of the geometric theory of functions of a complex variable on non-overlapping domains with free poles on radial systems. The main results of the present work strengthen and generalize several known results for this problem.

On a result of M. Heins

1975 ◽  
Vol 19 (4) ◽  
pp. 371-373 ◽  
Author(s):  
James A. Jenkins
Keyword(s):  
Riemann Surface ◽  
Simple Proof ◽  
Main Part ◽  
Plane Domain ◽  
Extremal Metric ◽  
Positive Genus ◽  
Closed Riemann Surface

Some years ago Heins (1) proved that a Riemann surface which can be conformally imbedded in every closed Riemann surface of a fixed positive genus g is conformally equivalent to a bounded plane domain. In the proof the main effort is required to prove that a surface satisfying this condition is schlichtartig. Heins gave quite a simple proof of the remaining portion (1; Lemma 1). The main part of the proof depended on exhibiting a family of surfaces of genus g such that a surface which could be conformally imbedded in all of them was necessarily schlichtartig. Another proof using a different construction was recently given by Rochberg (2). We will give here a further proof based on the method of the extremal metric and using a further construction which is in some ways more direct than those previously given.

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