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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A convergence theorem for Riemannian submanifolds
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by Zhong Min Shen PDF
Trans. Amer. Math. Soc. 347 (1995), 1343-1350 Request permission


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
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1343-1350
  • MSC: Primary 53C20; Secondary 53C15, 53C23, 53C30, 53C40
  • DOI:
  • MathSciNet review: 1254853