摘要:

We give a topological characterization of the sets that yield the maximalNth diameter among all the planar continua with unit capacity. At the same time we eliminate certain branching configurations for support points in the class ∑.

ISSN:0278-1077    

DOI:10.1080/17476938708814266

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814267

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814268

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Under certain conditions a two-dimensional harmonic mappinghcan be represented nontrivially ash=g-fwheref, gare both harmonic. On the basis of the current work, in conjunction with previous results, explicit formulas for the mappingsf, gfor which this is possible locally are obtained.

ISSN:0278-1077    

DOI:10.1080/17476938708814269

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

We begin with an extremal length problem which can be considered as a generalization of a problem of J. Hersch. To this problem there is associated an extremal region analogous to the extremal regions of Grotzsch, Teichmuller, and Mori. When the extremal length invariant is related to the harmonic measure invariant we obtain an inequality for harmonic measure which was first found by A. Ostrowski using a different definition of harmonic measure. We also show that our result implies Ostrowski's result.

ISSN:0278-1077    

DOI:10.1080/17476938708814270

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814271

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

So far, the only known sufficient condition for the existence of an extremal Teichmüller mapping with given boundary values is the frame mapping criterion. It assures, under certain conditions, the existence of an extremal mapping associated with a quadratic differential of finite norm. In this preliminary report, a sufficient condition will be given for the existence of an extremal Teichmüller mapping of the disk with infinitely many distinguished boundary points (called a polygon), if the frame mapping criterion fails.

ISSN:0278-1077    

DOI:10.1080/17476938708814272

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814273

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814255

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor