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Title: An application of moser iteration to complete minimal submanifolds in a sphere
Authors: Cheung, LF
Leung, PF
Issue Date: 2004
Publisher: Australian Mathematics Publ Assoc Inc
Source: Journal of the Australian mathematical society, 2004, v. 76, no. 2, p. 151-165 How to cite?
Journal: Journal of the Australian Mathematical Society 
Abstract: We apply the Moser iteration method to obtain a pointwise bound on the norm of the second fundamental form from a bound on its Ln norm for a complete minimal submanifold in a sphere. As an application we show that a complete minimal submanifold in a sphere with finite total curvature and Ricci curvature bounded away from -∞ must be compact. This complements similar results of Osserman and Oliveira in the case the ambient space is the Euclidean and the hyperbolic space respectively.
ISSN: 1446-7887
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