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The foundations of Minkowskian geometry

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Commentarii Mathematici Helvetici

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References

  1. H. Busemann, The geometry of Finsler spaces, Bull. Am. Math. Soc.

  2. H. Busemann, The isoperimetric problem for Minkowski area, Am. Journal Math., vol. 11 (1949), pp. 143–162.

    MathSciNet  Google Scholar 

  3. A. L. Underhill, Invariants of the functionF(x, y, x′, y′) in the calculus of variations, Trans. Am. Math. Soc. vol. 9 (1908) pp. 316–338.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Landsberg, Über die Krümmung in der Variationsrechnung, Math. Am. vol. 65 (1908) pp. 313–349.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Finsler, Über Kurven und Flächen in allgemeinen Räumen, Dissert. Göttingen 1918.

  6. K. Menger, Untersuchungen über allgemeine metrik. Vierte Untersuchung. Math. Ann. vol. 103 (1930) pp. 466–501.

    MathSciNet  MATH  Google Scholar 

  7. T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Berlin 1934

  8. H. Busemann, Intrinsic area, Ann. Math. vol. 48 (1947) pp. 234–267.

    Article  MathSciNet  Google Scholar 

  9. W. Blaschke, Vorlesungen über Differentialgeometrie II, Berlin 1923.

  10. D. A. Flanders, Angles between flat spaces of a realn-dimensional euclidean space, Studies and Essays presented to R. Courant, New York 1948, pp. 129–138.

  11. D. M. Y. Somerville, An introduction to the geometry ofN dimensions, London 1929.

  12. L. W. Fr. Meyer, Über die Anwendung eines Sylvesterschen Determinantensatzes aufein metrisches Problem desR n, Jahresber. Deutsch. Math. Ver., vol. 20 (1911) pp. 211–216.

    Google Scholar 

  13. P. Finsler, Über eine Verallgemeinerung des Satzes von Meusnier, Vierteljahrsschr. Naturf. Ges. Zürich, vol. 85 (1940) pp. 155–164.

    MathSciNet  Google Scholar 

  14. H. Busemann, A theorem on convex bodies of the Brunn-Minkowski type, Proc. Nat. Acad. Sc., vol. 35 (1949) pp. 27–31.

    Article  MATH  MathSciNet  Google Scholar 

  15. H. Busemann andW. Feller, Krümmungseigenschaften konvexer Flächen, Acta Math., vol. 66 (1936) pp. 1–47.

    Article  MathSciNet  Google Scholar 

  16. A. E. Taylor, A geometric theorem and its application to biorthogonal systems, Bull. Am. Math. Soc., vol. 53 (1947) pp. 614–616.

    Article  MATH  Google Scholar 

  17. H. Minkowski, Theorie der konvexen Körper, Ges. Abhandlungen, vol. 2, Leipzig 1911, pp. 131–229.

    Google Scholar 

  18. T. Radó, Length and area, Am. Math. Soc. Coll. Pub. vol. XXX (1948)

  19. E. Egerváry andG. Alexits, Fondements d’une théorie générale de la courbure linéaire, Comm. Math. Helv. vol. 13 (1941) pp. 257–276.

    Article  MATH  Google Scholar 

  20. A. Duschek and W. Mayer, Lehrbuch der Differential geometrie, vol. II Leipzig 1930.

  21. J. Haantjes, Distance geometry. Curvature in abstract metric spaces, Nederl. Akad. Wetensch Proc. 50 (1947) pp. 496–508.

    MATH  MathSciNet  Google Scholar 

  22. E. Cartan, Les espaces de Finsler, Exposées de Géométrie II, Paris 1934.

  23. W. Blaschke, Vorlesungen über Differentialgeometrie I, 2nd ed., Berlin 1924.

  24. E. Müller, Relative Minimalflächen, Monatsh. Math. Phys., vol. 31 (1921) pp. 3–19.

    Article  MATH  Google Scholar 

  25. A. Duschek, Über relative Flächentheorie, Sitzungsber. Akad. Wiss. Wien, vol. 135 (1926) pp. 1–8.

    Google Scholar 

  26. W. Fenchel and B. Jessen, Mengenfunktionen und konvexe Körper, Kgl. Danske Vid. Selskab, Math. Phys. Medd., vol. 16 (1938) No. 3

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Busemann, H. The foundations of Minkowskian geometry. Commentarii Mathematici Helvetici 24, 156–187 (1950). https://doi.org/10.1007/BF02567031

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