P. Pettersson
Differentiability of minimal geodesics in metrics of low regularity
(79K, Postscript)
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.