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Compactness analysis for free boundary minimal hypersurfaces

  • Lucas Ambrozio
  • Alessandro CarlottoEmail author
  • Ben Sharp
Article

Abstract

We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control.

Mathematics Subject Classification

Primary 53A10 Secondary 53C42 49Q05 

Notes

Acknowledgements

The authors wish to express their gratitude to André Neves for his interest in this work and for his constant support, and to the anonymous referee for carefully reading the manuscript and providing detailed feedback. A. C. also would like to thank Connor Mooney for several discussions and Francesco Lin for pointing out some relevant references. L. A. was visiting the University of Chicago while this article was written, and he would like to thank the Department of Mathematics for its hospitality. He is supported by the EPSRC on a Programme Grant entitled ‘Singularities of Geometric Partial Differential Equations’ reference number EP/K00865X/1.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  • Lucas Ambrozio
    • 1
  • Alessandro Carlotto
    • 2
    Email author
  • Ben Sharp
    • 1
  1. 1.University of WarwickCoventryUK
  2. 2.Department of MathematicsETH ZürichZürichSwitzerland

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