A convergence theorem for Riemannian submanifolds
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 Trans. Amer. Math. Soc. 347 (1995), 13431350 Request permission
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 pseudoholomorphic curves in symplectic manifolds.References

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Additional Information
 © Copyright 1995 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 347 (1995), 13431350
 MSC: Primary 53C20; Secondary 53C15, 53C23, 53C30, 53C40
 DOI: https://doi.org/10.1090/S00029947199512548530
 MathSciNet review: 1254853