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Stability of the cut locus in dimensions less than or equal to 6. (English) Zbl 0365.58010

MSC:
58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
58C25 Differentiable maps on manifolds
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References:
[1] Abraham, R., Robbin, J.: Transversal Mappings and Flows. New York-Amsterdam: Benjamin 1967 · Zbl 0171.44404
[2] Arnol’d, V.I.: Normal forms of functions with simple critical points, the Weyl groupsA k ,D k ,E k . and Lagrange maniforlds. Funct. Anal. and its Appl., Vol.6, No. 4, 3-25 (1972)
[3] Gromoll, D., Meyer, W.: On differentiable functions with isolated critical points. Topology 8, 361-369 (1969) · Zbl 0212.28903 · doi:10.1016/0040-9383(69)90022-6
[4] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. New York, London, Sydney: Interscience Publishers, 1969 · Zbl 0175.48504
[5] Mather, J.: Stability ofC ? mappings: I. The division theorem. Annals of Math. (2)87, 89-104 (1968) Stability ofC ? mappings: II. Infinitesimal stability implies stability, Annals of Math. (2)89, 254-291 (1969). Stability ofC ? mappings: III. Finitely determined map-germs, Publ. Math. I.H.E.S.35 127-156 (1968). Stability ofC ? mappings: V. Transversality, Advances in Math.4, 301-336 (1970) · Zbl 0159.24902 · doi:10.2307/1970595
[6] Milnor, J.: Morse Theory. Annals of Math. Studies No. 51. Princeton: University Press 1963 · Zbl 0108.10401
[7] Siersma, D.: Classification and deformation of Singularities. Amsterdam: Thesis 1974 · Zbl 0283.57012
[8] Mather, J.: Stratifications and Mappings, Dynamical Systems. New York, London: Academic Press 1973 · Zbl 0286.58003
[9] Whitney, H.: Elementary structure of real algebraic varieties. Ann. of Math.66, 545-556 (1957) · Zbl 0078.13403 · doi:10.2307/1969908
[10] Buchner, M.: Triangulation of the real analytic cut locus. To appear in Proc. of the Am. Math. Soc. · Zbl 0373.53020
[11] Buchner, M.: Structure of the cut locus in dimensions less than or equal to 6. To appear in Compositio Mathematica · Zbl 0365.58010
[12] Gluck, H., Singer, D.: Deformations of Geodesic Fields. To appear · Zbl 0334.53047
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