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

页码：151 / 177

页数：27

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