Geodesics on Non–complete Finsler Manifolds
نویسنده
چکیده
In this note based on paper [3] we deal with domains D (i.e. connected open subsets) of a Finsler manifold (M, F ). At first we carry out a comparison between different notions of convexity for their boundaries. Then a careful application of variational methods to the geodesic problem yields that the convexity of ∂D is equivalent to the existence of a minimal geodesic for each pair of points of D. Furthermore multiplicity of connecting geodesics can be obtained if D is not contractible.
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