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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

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The analyticity of distance function

Given a real analytic compact manifold $M$ with boundary $\partial M$, suppose that $M$ is embedded in an open analytic manifold $N$ which has the same dimension as $M$. Is the distance function $d(x …