×

A geometrical theory of multiple integral problems in the calculus of variations. (English) Zbl 0232.49010


MSC:

49Q15 Geometric measure and integration theory, integral and normal currents in optimization
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Cartan, E.,Les espaces de Finsler (Hermann, Paris, 1934). · Zbl 0008.41805
[2] Davies, E. T.,Areal Spaces, Ann. Mat. Pura Appl. (4)55, 63–76 (1961). · Zbl 0108.17303 · doi:10.1007/BF02412076
[3] Douglas, J.,Systems of K-Dimensional Manifolds in an N-Dimensional Space, Math. Ann.105, 707–733 (1931). · Zbl 0003.16902 · doi:10.1007/BF01455841
[4] Kawaguchi, A.,On Areal Spaces. I. Metric Tensors in n-Dimensional Spaces Based on the Notion of Two-Dimensional Area, Tensor (N.S.)1, 14–15 (1950). · Zbl 0041.50104
[5] Kawaguchi, A.,On Areal Spaces. II. Introduction to the Theory of Connections in n-Dimensional Spaces of the Submetric Class, Tensor (N.S.)1, 67–88 (1951). · Zbl 0044.37201
[6] Kawaguchi, A.,On Areal Spaces. III. The Metric m-Tensor in n-Dimensional Areal Spaces Based on the Notion of m-Dimensional Area and Connections in the Submetric Areal Spaces, Tensor (N.S.)1, 89–103 (1951). · Zbl 0044.37202
[7] Kawaguchi, A. andKatsurada, Y.,On Areal Spaces. IV. Connection Parameters in an Areal Space of General Type, Tensor, (N.S.)1, 137–156 (1951). · Zbl 0045.43601
[8] Kawaguchi, A. andTandai, K.,On Areal Spaces. V. Normalized Metric Tensor and Connection Parameters in a Space of the Submetric Class, Tensor (N.S.)2, 47–58 (1952). · Zbl 0049.23601
[9] Tandai, K.,On Areal Spaces. VI. On the Characterization of Metric Areal Spaces, Tensor (N.S.)3, 40–45 (1953). · Zbl 0051.39603
[10] Tandai, K.,On Areal Spaces. VII. The Theory of the Canonical Connection and m-Dimensional Subspaces, Tensor (N.S.)4, 78–90 (1954). · Zbl 0058.16101
[11] Tandai, K.,On Areal Spaces. VIII. Theory of a Space of the Semimetric Class, Tensor (N.S.)10, 161–166 (1960). · Zbl 0091.34901
[12] Rund, H.,The Differential Geometry of Finsler Spaces (Springer Verlag, Berlin, 1959). · Zbl 0087.36604
[13] Rund, H.,The Hamilton-Jacobi Theory in the Calculus of Variations: Its Role in Mathematics and Physics (Van Nostrand, London–New York, 1966). · Zbl 0141.10602
[14] Rund, H.,A Geometrical Theory of Multiple Integral Problems in the Calculus of Variations, Canad. J. Math.20, 639–657 (1968). · Zbl 0155.44301 · doi:10.4153/CJM-1968-062-1
[15] Su, Buchin,The Geometry of Spaces with Areal Metrics, Math. Nachr.16, 281–287 (1957). · Zbl 0080.15103 · doi:10.1002/mana.19570160504
[16] Su, Buchin,On the Theory of Affine Connections in an Areal Space, Bull. Math. Soc. Sci. Math. Phys. R. P. Roumaine (N.S.)2 (50), 185–190 (1958). · Zbl 0090.12604
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.