Geodesic
A Brunn-Minkowski Type Theorem on the Minkowski Spacetime
Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 449-469

Voir la notice de l'article provenant de la source Cambridge University Press

In this article, we derive a Brunn-Minkowski type theorem for sets bearing some relation to the causal structure on the Minkowski spacetime ${{\mathbb{L}}^{n+1}}$ . We also present an isoperimetric inequality in the Minkowski spacetime ${{\mathbb{L}}^{n+1}}$ as a consequence of this Brunn-Minkowski type theorem.
DOI : 10.4153/CJM-1999-020-0
Mots-clés : 53B30, 52A40, 52A38, Minkowski spacetime, Brunn-Minkowski inequality, isoperimetric inequality 
Bahn, Hyoungsick; Ehrlich, Paul. A Brunn-Minkowski Type Theorem on the Minkowski Spacetime. Canadian journal of mathematics, Tome 51 (1999) no. 3, pp. 449-469. doi: 10.4153/CJM-1999-020-0
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[B] [B] Bahn, H., Isoperimetric Inequalities and Conjugate Points on Lorentzian Surfaces. J. Geom. (to appear). Google Scholar

[BH] [BH] Bahn, H. and Hong, S., Isoperimetric inequalities for sectors on the Minkowski 2-spacetime. J. Geom. (to appear). Google Scholar

[Ba] [Ba] Bandle, C., Isoperimetric Inequalities and applications. Pitman, London, 1980. Google Scholar

[BB] [BB] Beckenbach, E. and Bellman, R., Inequalities. Springer-Verlag, Berlin, 1961. Google Scholar

[BEE] [BEE] Beem, J., Ehrlich, P. and Easley, K., Global Lorentzian Geometry. 2nd ed., Dekker, New York, 1996. Google Scholar

[Bl] [Bl] Bloom, D., Linear algebra and geometry. Cambridge Univ. Press, Cambridge, 1979. Google Scholar

[BF] [BF] Bonnesen, T. andFenchel, W., Theorie der konvexen Körper. Springer-Verlag, Berlin, 1934. Google Scholar

[BZ] [BZ] Burago, Yu. D. and Zalgaller, V. A., Geometric Inequalities. Springer-Verlag, Berlin, 1988. Google Scholar

[F] [F] Federer, H., Geometric Measure Theory. Springer-Verlag, New York, 1969. Google Scholar

[Hs] [Hs] Hsiung, C.-C., Some integral formulas for closed hypersurfaces. Math. Scand. 2 (1954), 286–294. Google Scholar

[LP] [LP] Lions, P. L. and Pacella, F., Isoperimetric inequalities for convex cones. Proc. Amer. Math. Soc. 109 (1990), 477–485. Google Scholar

[On] [On] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity. Academic Press, New York, 1983. Google Scholar

[W] [W] Webster, R., Convexity. Oxford Univ. Press, Oxford, 1994. Google Scholar

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