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Intrinsic distance on a Lipschitz Riemannian manifold. (Italian. English summary) Zbl 0719.53047

Summary: The classical concept of length of a curve and hence of intrinsic distance induced by a Riemannian metric is extended to LIP manifolds with LIP Riemannian metric. The main difficulties arise from the fact that neither the changes of charts are differentiable nor the metric verifies the ellipticity condition everywhere, but only almost everywhere.

MSC:

53C70 Direct methods (\(G\)-spaces of Busemann, etc.)
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