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.
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页码：223 / 231
页数：9
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