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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A convergence theorem for Riemannian submanifolds


Author: Zhong Min Shen
Journal: Trans. Amer. Math. Soc. 347 (1995), 1343-1350
MSC: Primary 53C20; Secondary 53C15, 53C23, 53C30, 53C40
MathSciNet review: 1254853
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Abstract: In this paper we study the convergence of Riemannian submanifolds. In particular, we prove that any sequence of closed submanifolds with bounded normal curvature and volume in a closed Riemannian manifold subconverge to a closed submanifold in the $ {C^{1,\alpha }}$ topology. We also obtain some applications to irreducible homogeneous manifolds and pseudo-holomorphic curves in symplectic manifolds.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1254853-0
PII: S 0002-9947(1995)1254853-0
Keywords: Riemannian submanifold, convergence in the $ {C^{1,\alpha }}$ topology, normal curvature, volume, isoperimetric inequality, injectivity radius, pseudo-holomorphic curve, homogeneous manifold
Article copyright: © Copyright 1995 American Mathematical Society