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The paper describes some qualitative properties of minimizerson a manifold M endowed with a discontinuous metric. The discontinuityoccurs on a hypersurface disconnecting M. Denote by 1 and2 the open subsets of M such that M\ =12. Assume that and are endowed with metrics ·, · (1) and ·,·(2), respectively, such that (i=1, 2) is convex or concave. The existence of a minimizerof the length functional on curves joining two given pointsof M is proved. The qualitative properties obtained allows therefraction law in a very general situation to be described.  相似文献   
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An analytical theory for Riemannian cubic polynomials   总被引:3,自引:0,他引:3  
We establish some global existence and multiplicity resultsfor Riemannian cubic polynomials in a complete Riemannian manifold.  相似文献   
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