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Curvature restrictions on convex, timelike surfaces in Minkowski 3-space


Author: Senchun Lin
Journal: Proc. Amer. Math. Soc. 128 (2000), 1459-1466
MSC (1991): Primary 53C42, 53C40, 53B30
DOI: https://doi.org/10.1090/S0002-9939-99-05533-1
Published electronically: December 8, 1999
MathSciNet review: 1709760
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Abstract: Suppose that $K$ and $H$ are Minkowski Gauss curvature and Minkowski mean curvature respectively on a timelike surface $S$ that is $C^{2}$ immersed in Minkowski 3-space $E^{3}_{1}$. Suppose also that $0\not \equiv K < 0$ and that $S$ is complete as a surface in the underlying Euclidean 3-space $E^{3}$. It is shown that neither $K$ nor $H$ can be bounded away from zero on such a surface $S$.


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Additional Information

Senchun Lin
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: senchun@math.rutgers.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05533-1
Received by editor(s): June 23, 1998
Published electronically: December 8, 1999
Communicated by: Peter Li
Article copyright: © Copyright 2000 American Mathematical Society

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