The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 1344–1386 | Cite as

Immersions with Bounded Second Fundamental Form

  • Patrick BreuningEmail author


We first consider immersions on compact manifolds with uniform L p -bounds on the second fundamental form and uniformly bounded volume. We show compactness in arbitrary dimension and codimension, generalizing a classical result of J. Langer. In the second part, this result is used to deduce a localized version, being more convenient for many applications, such as convergence proofs for geometric flows.


Immersions Compactness Second fundamental form Bounded curvature Compact and noncompact manifolds 

Mathematics Subject Classification

53C42 53C23 53B25 



I would like to thank my advisor Ernst Kuwert for his support. Moreover, I would like to thank Manuel Breuning for proofreading my dissertation [6], where the results of this paper were established first.


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© Mathematica Josephina, Inc. 2014

Authors and Affiliations

  1. 1.Fakultät für Mathematik des Karlsruher Institut für TechnologieInstitut für AnalysisKarlsruheGermany

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