Acta Mathematica
- Acta Math.
- Volume 148 (1982), 47-157.
Calibrated geometries
Reese Harvey and H. Blaine Lawson
Full-text: Open access
Note
Research supported by NSF Grants MPS75-05270 and GP-23785X2.
Article information
Source
Acta Math., Volume 148 (1982), 47-157.
Dates
Received: 16 March 1981
First available in Project Euclid: 31 January 2017
Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890157
Digital Object Identifier
doi:10.1007/BF02392726
Mathematical Reviews number (MathSciNet)
MR666108
Zentralblatt MATH identifier
0584.53021
Rights
1982 © Almqvist & Wiksell
Citation
Harvey, Reese; Lawson, H. Blaine. Calibrated geometries. Acta Math. 148 (1982), 47--157. doi:10.1007/BF02392726. https://projecteuclid.org/euclid.acta/1485890157
References
- Arnold, V. I., Mathematical Methods of Classical Mechanics. Springer-Verlag, New York, 1978.Zentralblatt MATH: 0386.70001
- Berger, M., Sur les groups d'holonomie homogene des varieties à connexion affine et des varietie riemanniennes. Bull. Soc. Math. France, 83 (1955), 279–330.
- —, Du côté de chez pu. Ann. Sci. École Norm. Sup., 5 (1972), 1–44.Zentralblatt MATH: 0227.52005
- Bombieri, E., Algebraic values of meromorphic maps. Invent. Math., 10 (1970), 267–287.Zentralblatt MATH: 0214.33702
Mathematical Reviews (MathSciNet): MR306201
Digital Object Identifier: doi:10.1007/BF01418775 - Bryant, R. L., Submanifolds and special structures on the octonions. J. Differential Geom., 17 (1982).
- Brown, R. & Gray, A., Vector cross products. Comment. Math. Helv., 42 (1967), 222–236.
- Calabi, E., Construction and some properties of some 6-dimensional almost complex manifolds. Trans. Amer. Math. Soc., 87 (1958), 407–438.Zentralblatt MATH: 0080.37601
Mathematical Reviews (MathSciNet): MR130698
Digital Object Identifier: doi:10.2307/1993108 - Curtis, C. W., The four and eight square problem and division algebras, in Studies in modern algebra, Vol. 2 MAA Studies in Mathematics (1963), 100–125.
- Do Carmo M. & Wallach, N. R., Representations of compact groups and minimal immersions into spheres. J. Differential Geom., 4 (1970), 91–104.Zentralblatt MATH: 0197.18301
- Federer, H., Geometric Measure Theory, Springer-Verlag, New York, 1969.Zentralblatt MATH: 0176.00801
- —, Real flat chains, cochains and variational problems. Indiana Univ. Math. J., 24 (1974), 351–407.Zentralblatt MATH: 0289.49044
Mathematical Reviews (MathSciNet): MR348598
Digital Object Identifier: doi:10.1512/iumj.1974.24.24031 - —, Colloquium lectures on geometric measure theory. Bull. Amer. Math. Soc., 84 (1978), 291–338.
- Federer, H. & Fleming, W. H., Normal and integral currents. Ann. of Math., 72 (1960), 458–520.Zentralblatt MATH: 0187.31301
Mathematical Reviews (MathSciNet): MR123260
Digital Object Identifier: doi:10.2307/1970227 - Gray, A., Vector cross products on manifolds. Trans. Amer. Math. Soc., 141 (1969), 465–504.Zentralblatt MATH: 0182.24603
Mathematical Reviews (MathSciNet): MR243469
Digital Object Identifier: doi:10.2307/1995115 - Harvey, R., Removable singularities for positive currents. Amer. J. Math., 96 (1974), 67–78.Zentralblatt MATH: 0293.32015
Mathematical Reviews (MathSciNet): MR361156
Digital Object Identifier: doi:10.2307/2373581 - —, Holomorphic chains and their boundaries, Proceedings of Symposia in Pure Mathematics, 30∶1. A.M.S., Providence, R.I. (1977), 309–382.
- Harvey, R. & King, J., On the structure of positive currents. Invent. Math., 15 (1972), 47–52.Zentralblatt MATH: 0235.32006
Mathematical Reviews (MathSciNet): MR296348
Digital Object Identifier: doi:10.1007/BF01418641 - Harvey, R. & Knapp, A. W., Positive (p, p)-forms, Wirtinger's inequality and currents, value distribution theory, Part A. Proceedings Tulane University. Program on Value-Distribution Theory in Complex Analysis and Related Topics in Differential Geometry, 1972–1973, pp. 43–62. Dekker, New York, 1974.
- Harvey, R. & Lawson, Jr., H. B., On boundaries of complex analytic varieties, I. Ann. of Math., 102 (1975), 233–290.
- —, On boundaries of complex analytic varieties, II. Ann. of Math., 106 (1977), 213–238.Zentralblatt MATH: 0361.32010
Mathematical Reviews (MathSciNet): MR499285
Digital Object Identifier: doi:10.2307/1971093 - Harvey, R., A constellation of minimal varieties defined over the group G2. Proceedings of Conference on Geometry and Partial Differential Equations, Lecture Notes in Pure and Applied Mathematics, 48. Marcel-Dekker (1979), 167–187.
- —, Geometries associated to the group SUn and varieties of minimal submanifolds arising from the Cayley arithmetic, in Minimal submanifolds and geodesics. Kaigai Publications, Tokyo (1978), 43–59.
- —, Calibrated foliations. Amer. J. Math., 103 (1981), 411–435.
- Harvey, R. & Polking, J., Removable singularities of solutions of linear partial differential equations. Acta Math., 125 (1970), 39–56.Zentralblatt MATH: 0214.10001
Mathematical Reviews (MathSciNet): MR279461
Digital Object Identifier: doi:10.1007/BF02838327 - —, Extending analytic objects. Comm. Pure Appl. Math., 28 (1975), 701–727.
- Harvey, R. & Shiffman, B., A characterization of holomorphic chains. Ann. of Math., 99 (1974), 553–587.Zentralblatt MATH: 0287.32008
Mathematical Reviews (MathSciNet): MR355095
Digital Object Identifier: doi:10.2307/1971062 - Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York, 1978.Zentralblatt MATH: 0451.53038
- Hsiang, W. Y. & Lawson, Jr., H. B., Minimal submanifolds of low cohomogeneity. J. Differential Geom., 5 (1971), 1–38.
- King, J., The currents defined by analytic varieties. Acta Math., 127 (1971), 185–220.Zentralblatt MATH: 0224.32008
Mathematical Reviews (MathSciNet): MR393550
Digital Object Identifier: doi:10.1007/BF02392053 - Kleinfeld, E., A characterization of the Cayley numbers, in Studies in modern algebra, Vol. 2 MAA Studies in Mathematics (1963), 126–143.
- Kobayashi, S. & Nomizu, K., Foundations of Differential Geometry, I and II. Wiley-Interscience, New York, 1963 and 1969.
- Lawson, Jr., H. B., Complete minimal surfaces in S3. Ann. of Math., 92 (1970), 335–374.Zentralblatt MATH: 0205.52001
Mathematical Reviews (MathSciNet): MR270280
Digital Object Identifier: doi:10.2307/1970625 - —, The equivariant Plateau problem and interior regularity. Trans. Amer. Math. Soc., 173 (1972), 231–250.Zentralblatt MATH: 0279.49043
Mathematical Reviews (MathSciNet): MR308905
Digital Object Identifier: doi:10.2307/1996271 - —, Foliations. Bull. Amer. Math. Soc., 80 (1974), 369–417.
- —, Minimal varieties in real and complex geometry. University of Montreal Press, Montreal 1973.Zentralblatt MATH: 0328.53001
- Lawson, Jr., H. B. & Osserman, R., Non-existence, non-uniqueness and irregularity of solutions to the minimal surface system. Acta Math., 139 (1977), 1–17.Zentralblatt MATH: 0376.49016
Mathematical Reviews (MathSciNet): MR452745
Digital Object Identifier: doi:10.1007/BF02392232 - Lelong, P., Fonctions plurisousharmoniques et formes differentielles positives. Gordon and Breach, New York; distributed by Dunod Éditeur, Paris, 1968.Zentralblatt MATH: 0195.11603
- Lelong, P., Sur la structure des courants positifs fermés. Séminaire Pierre Lelong, Lecture Notes in Mathematics, 578. Springer (1975/76), 136–156.
- Lewy, H., On the non-vanishing of the Jacobian of a homeomorphism by harmonic gradients, Ann. of Math., 88 (1968), 578–529.
- Morrey, C. B., Second order elliptic systems of partial differential equations, pp. 101–160, in Contributions to the Theory of Partial Differential Equations. Ann. of Math. Studies, 33, Princeton Univ. Press, Princeton, 1954.
- Ruelle, D. & Sullivan, D., Currents, flows and diffeomorphisms. Topology, 14 (1975), 319–327.Zentralblatt MATH: 0321.58019
Mathematical Reviews (MathSciNet): MR415679
Digital Object Identifier: doi:10.1016/0040-9383(75)90016-6 - Simons, J., On transitivity holonomy systems. Ann of Math., 76 (1962), 213–234.Zentralblatt MATH: 0106.15201
Mathematical Reviews (MathSciNet): MR148010
Digital Object Identifier: doi:10.2307/1970273 - Siu, Y. T., Analyticity of sets associated to Lelong numbers and the extension of closed positive currents. Invent. Math., 27 (1974), 53–156.Zentralblatt MATH: 0289.32003
Mathematical Reviews (MathSciNet): MR352516
Digital Object Identifier: doi:10.1007/BF01389965 - Spivak, M., Differential geometry, V. Publish or Perish, Berkeley 1979.
- Yau, S. T., Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A., 74 (1977), 1798–1799.Zentralblatt MATH: 0355.32028
Mathematical Reviews (MathSciNet): MR451180
Digital Object Identifier: doi:10.1073/pnas.74.5.1798

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