01-400 P. Pettersson

Differentiability of minimal geodesics in metrics of low regularity (79K, Postscript) Oct 30, 01

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Abstract. In Riemannian metrics that are only H lder continuous of order s, 0 <= s <= 1, let minimal geodesics be the continuous curves realizing the shortest distance between two points. It is shown that for 0 < s <= 1, minimal geodesics are differentiable with a derivative which is at least H lder continuous of order s/2 for 0 < s < 1 and which is H lder continuous of order 1 for s = 1.

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