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Locally Euclidean metrics with a given geodesic curvature of the boundary. (English. Russian original) Zbl 1180.53016

Proc. Steklov Inst. Math. 266, 210-218 (2009); translation from Tr. Mat. Inst. Steklova 266, 218-226 (2009).
Summary: The problem of reconstructing a locally Euclidean metric on a disk from the geodesic curvature of the boundary given in the metric sought after is considered. This problem is an analog and a generalization of the classical problem of finding a closed plane curve from its curvature given as a function of the arc length. The solution of this problem in our approach can be interpreted as finding a plane domain with the standard Euclidean metric whose boundary has a given geodesic curvature.

MSC:

53B20 Local Riemannian geometry
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