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|Title:||An application of moser iteration to complete minimal submanifolds in a sphere|
|Source:||Cheung, L.-F.,Leung, P.-F. (2004-04). An application of moser iteration to complete minimal submanifolds in a sphere. Journal of the Australian Mathematical Society 76 (2) : 151-165. ScholarBank@NUS Repository.|
|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.|
|Source Title:||Journal of the Australian Mathematical Society|
|Appears in Collections:||Staff Publications|
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