Extremal properties of the principal Dirichlet eigenvalue for regular polygons in the hyperbolic plane

被引：5

作者：

Karp, L

Peyerimhoff, N

机构：

[1] CUNY, Grad Ctr, Dept Math, New York, NY 10016 USA

[2] CUNY Herbert H Lehman Coll, Dept Math, New York, NY 10016 USA

[3] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

来源：

ARCHIV DER MATHEMATIK | 2002年 / 79卷 / 03期

关键词：

Fixed Base; Hyperbolic Plane; Geometric Description; Unique Minimum; Regular Polygon;

D O I：

10.1007/s00013-002-8308-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that amongst all hyperbolic triangles of equal perimeter or quadrilaterals in a given geodesic ball the regular polygon is the unique minimum for the first Dirichlet eigenvalue. Moreover, we give a geometric description of the set of all hyperbolic triangles with a fixed base and prescribed area.

引用

页码：223 / 231

页数：9

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