On scalar metrics that maximize geodesic distances in the plane

Conti, Sergio; Schweizer, Ben
May 2011
Calculus of Variations & Partial Differential Equations;May2011, Vol. 41 Issue 1/2, p151
Academic Journal
Riemannian metric a in the plane together with a point $${A\subset \mathbb {R}^2}$$ induces a distance function d( 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.


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