Author： Arcostanzo M. Michel R.
Publisher： Springer Publishing Company
ISSN： 0046-5755
Source： Geometriae Dedicata, Vol.76, Iss.2, 1999-07, pp. : 197-209
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Abstract
We give a geometrical proof of a Muhometov type inequality, for a single Riemannian metric defined on a closed disc in the plane. We mainly study the case of equality which is achieved if and only if the distance between points on the boundary is invariant under rotation along the boundary. We show that this implies that the metric itself must be invariant under rotation, at least when the metric is analytic or of nonpositive curvature.
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