Let $(M, g)$ be a (Cauchy) complete Riemannian surface with boundary and fix a point $p \in M \setminus \partial M$. Is there a minimizing geodesic from $p$ to $\partial M$? I believe this is true, but I am not used to working with geodesics in this context.
2026-03-28 01:47:20.1774662440
Minimizing geodesic in sufaces with boundary
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