×

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
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[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
[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
[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
[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
[18] M. SPIVAK , A Comprehensive Introduction to Differential Geometry , Vol. 5, Publish or Perish, 1975 . Zbl 0306.53003 · Zbl 0306.53003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.