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4 votes

The existence of length-minimizing path between two points in a Riemannian manifold with bou...

Alexander, Berg, Bishop: The Riemannian obstacle problem. https://projecteuclid.org/download/pdf_1/euclid.ijm/1255989406
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2 votes

Groups of conformal isomorphisms of simply connected surfaces

After postcomposing with a suitable Möbius transformation one can assume that f maps infinity to infinity. So f is an entire function on the complex plane. By Casorati-Weierstrass (or Picard), it cann …
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