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On the average curvature of a convex curve in a surface of nonpositive Gaussian curvature

Author(s): Jin Lu
Journal: Proc. Amer. Math. Soc. 130 (2002), 3693-3699.
MSC (2000): Primary 53C45, 58A05; Secondary 52A10, 52A40
Posted: May 1, 2002
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Abstract | References | Similar articles | Additional information

Abstract: In this paper, the upper bound of the average curvature of a convex curve in a simply connected surface of nonpositive Gaussian curvature is obtained.

References:

1.: M.Bridgeman, Average curvature of convex curves in $H^{2}$ , Proc. Amer. Math. Soc., 126(1998), 221-224. MR 98c:52012
2.: W.Klingenberg, A course in differential geometry, Springer-Verlag, New York, 1978. MR 57:13702
3.: W.Klingenberg, D.Gromoll and W.Meyer, Riemannsche geometrie in Grossen, Springer-Verlag, Berlin, 1968. MR 37:4751
4.: H.Wu, C.L.Shen and Y.L.Yu, Introduction of Riemannian geometry (Chinese), Beijing University Press, Beijing, 1989.

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Additional Information:

Jin Lu
Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, People's Republic of China
Email: jinluk@online.sh.cn

DOI: 10.1090/S0002-9939-02-06511-5
PII: S 0002-9939(02)06511-5
Keywords: Average curvature, curve, surface
Received by editor(s): October 13, 2000
Received by editor(s) in revised form: July 11, 2001
Posted: May 1, 2002
Additional Notes: This work was supported by the Chinese NNSF
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2002, American Mathematical Society


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