Some extremal problems on the hyperbolic polygons
作者:
A. Yu. Solynin,
期刊:
Complex Variables, Theory and Application: An International Journal
(Taylor Available online 1998)
卷期:
Volume 36,
issue 3
页码: 207-231
ISSN:0278-1077
年代: 1998
DOI:10.1080/17476939808815110
出版商: Gordon and Breach Science Publishers
关键词: Hyperbolic poligon;conformal radius;reduced module of a triangle;;capacity;dissymmetrization;30C75;30C85;31A15
数据来源: Taylor
摘要:
We study some isoperimetric problems for plane polygons. In particular we show that among all hyperbolicn-gons with a fixed number of sides the regular one has the maximal value of the ratio “conformal radius : perimeter”. Forn-gon admitting a fulln-sides reflection by theamplification coefficientwe mean the ratio of the conformal radii of given and reflected polygons. We prove that the amplification coefficient takes the minimal value only for the regularn-gons, that confirms the conjecture posed by J. Hersch [6].
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