On scalar metrics that maximize geodesic distances in the plane

被引：1
|
作者：
Conti, Sergio [1 ]
Schweizer, Ben [2 ]
机构：
[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany
[2] Tech Univ Dortmund, Fak Math, D-44227 Dortmund, Germany
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 41卷 / 1-2期
关键词：
GAMMA-CONVERGENCE; ENERGY; LIMIT;
D O I：
10.1007/s00526-010-0357-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A Riemannian metric a in the plane together with a point A subset of R-2 induces a distance function d(a)(A, .). We investigate the optimization problem searching a scalar metric a which maximizes the distance between A and a given set B. We find necessary conditions for optimal metrics which help to determine solutions a. In the case that the set B is a single point, we determine the optimal metric explicitly.
引用
收藏
页码：151 / 177
页数：27
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