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Sobolev Inequalities Relating Rough Riemannian Metrics to their Distance Functions
In previous papers, the first named author and E. Bryden explored Sobolev like inequalities relating the norm of a Riemmanian metric $g_1$, in terms of a background Riemannian metric $g_0$, in order to estimate the distance function $d_{g_1}$. Although $|g_1|_{g_0}$ is not the gradient of the distan
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