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Some regularity theorems in Riemannian geometry. (English) Zbl 0486.53014

MSC:
53B20 Local Riemannian geometry
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
35B65 Smoothness and regularity of solutions to PDEs
35J60 Nonlinear elliptic equations
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[1] L. BERS , F. JOHN and M. SCHECHTER , Partial Differential Equations , John Wiley, 1964 (later reprinted by Amer. Math. Soc.). MR 29 #346 | Zbl 0126.00207 · Zbl 0126.00207
[2] E. CALABI and P. HARTMAN , On the Smoothness of Isometries (Duke Math. J., Vol. 37, 1970 , pp. 741-750). Article | MR 44 #957 | Zbl 0203.54304 · Zbl 0203.54304 · doi:10.1215/S0012-7094-70-03789-0 · minidml.mathdoc.fr
[3] E. CARTAN , Sur la possibilité de plonger un espace riemannien donné dans un espace euclidien (Ann. Soc. Pol. Math., Vol. 6, 1927 , pp. 1-17). JFM 54.0763.05 · JFM 54.0763.05
[4] D. DETURCK , Metrics With Prescribed Ricci Curvature [Proceedings of I.A.S. Differential Geometry Seminar, 1979 - 1980 (to appear in Annals of Math. series)].
[5] D. DETURCK , Existence of Metrics With Prescribed Ricci Curvature : Local Theory (to appear). · Zbl 0489.53014 · doi:10.1007/BF01389010 · eudml:142846
[6] A. EINSTEIN , Näherungsweise Integration der Feldgleichungen der Gravitation (S.-B. Preuss. Akad. Wiss., 1916 , pp. 688-696). JFM 46.1293.02 · JFM 46.1293.02
[7] A. FISCHER and J. MARSDEN , General Relativity, Partial Differential Equations, and Dynamical Systems (Proc. Symp. Pure Math., Vol. 28 ; Amer. Math. Soc., 1973 , pp. 309-327). MR 53 #11656 | Zbl 0262.35035 · Zbl 0262.35035
[8] R. GREENE and H. WU , Embedding of Open Riemannian Manifolds by Harmonic Functions (Ann. Inst. Fourier, Grenoble, Vol. 25, 1975 , pp. 215-235). Numdam | MR 52 #3583 | Zbl 0307.31003 · Zbl 0307.31003 · doi:10.5802/aif.549 · numdam:AIF_1975__25_1_215_0 · eudml:74211
[9] P. HARTMAN , On Geodesic Coordinates (American J. Math., Vol. 73, 1951 , pp. 949-954). MR 13,683e | Zbl 0044.17306 · Zbl 0044.17306 · doi:10.2307/2372125
[10] M. JANET , Sur la possibilité de plonger un espace riemannien donné dans un espace euclidien (Ann. Soc. Pol. Math., Vol. 5, 1926 , pp. 38-42). JFM 53.0699.01 · JFM 53.0699.01
[11] J. KAZDAN , Another Proof of Bianchi’s Identity in Riemannian Geometry (to appear in Proc. Amer. Math. Soc., 1981 ). MR 82b:53026 | Zbl 0459.53033 · Zbl 0459.53033 · doi:10.2307/2044224
[12] J. KAZDAN and F. WARNER , Curvature Functions for Open 2-Manifolds (Ann. Math., Vol. 199, 1974 , pp. 203-219). MR 49 #7950 | Zbl 0278.53031 · Zbl 0278.53031 · doi:10.2307/1970898
[13] S. KOBAYASHI and K. NOMIZU , Foundations of Differential Geometry , Vol. I, Interscience, New York, 1964 . Zbl 0119.37502 · Zbl 0119.37502
[14] C. LANCZOS , Ein Vereinfachendes Koordinatensystem für die Einsteinschen Gravitationsgleichungen (Phys. Z., Vol. 23, 1922 , pp. 537-539). JFM 48.1023.01 · JFM 48.1023.01
[15] B. MALGRANGE , Sur l’intégrabilité des structures presque-complexes (Symposia Math., Vol. II, I.N.D.A.M., Rome, 1968 , Academic Press, London, 1969 , pp. 289-296). MR 40 #6598 | Zbl 0186.42504 · Zbl 0186.42504
[16] C. MORREY , Jr. , Multiple Integrals in the Calculus of Variations (Grund. der Math. Wiss., Vol. 133, Springer-Verlag, New York, 1966 ). Zbl 0142.38701 · Zbl 0142.38701
[17] S. D. MYERS , Riemannian Manifolds in the Large (Duke Math. J., Vol. 1, 1935 , pp. 39-49). Article | Zbl 0011.22502 | JFM 61.0786.03 · Zbl 0011.22502 · doi:10.1215/S0012-7094-35-00105-3 · minidml.mathdoc.fr
[18] M. SPIVAK , A Comprehensive Introduction to Differential Geometry , Vol. 5, Publish or Perish, 1975 . Zbl 0306.53003 · Zbl 0306.53003
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