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On the affine diameter of closed convex hypersurfaces

Published online by Cambridge University Press:  17 April 2009

Weimin Sheng  and
Neil S. Trudinger
Weimin Sheng
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310028, Peoples Republic of China, e-mail: [email protected]
Neil S. Trudinger
Affiliation:
Centre for Mathematics and Its Applications, The Australian National University, Canberra, ACT 0200, Australia, e-mail: [email protected]
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Abstract

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In this paper we prove that the affine diameter of any closed uniformly convex hypersurface in Euclidean space enclosing finite volume is bounded from above.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 431 - 437
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Blaschke, W., Vorlesungen über Differentialgeometrie (Berlin, 1923).Google Scholar
[2]Gutiérrez, C.E., The Monge-Ampère equation (Birkhäuser, Boston M.A., 2001).Google Scholar
[3]De Guzman, M., Differentiation of integrals in Rn, Lecture Notes in Math. 481 (Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[4]van Heijenoort, J., ‘On locally convex manifolds’, Comm. Pure Appl. Math. 5 (1952), 223–242.Google Scholar
[5]Li, A.M., Simon, U. and Zhao, G., Global affine differential geometry of hypersurfaces, Gruyter Exponsition in Mahts 11 (Walter de Gruyter, Berlin, 1993).Google Scholar
[6]Nomizu, K. and Sasaki, T., Affine differential geometry, Cambridge Tracts in Mathematics 111 (Cambridge University Press, Cambridge, 1994).Google Scholar
[7]Sacksteder, R., ‘On hypersurfaces with no negative sectional curvatures’, Amer. J. Math. 82 (1960), 609–630.Google Scholar
[8]Trudinger, N.S. and Wang, X.-J., ‘Affine complete locally convex hypersurfaces’, Invent. Math. 150 (2002), 45–60.Google Scholar
[9]Trudinger, N.S. and Wang, X.-J., ‘On locally convex hypersurfaces with boundary’, J. Reine Angew. Math. 551 (2002), 11–32.Google Scholar