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Compactness and
generic finiteness for free boundary minimal hypersurfaces,
I
Qiang Guang, Zhichao Wang and Xin Zhou |
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Vol. 310 (2021), No. 1, 85–114
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Abstract |
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Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical convergence away from finitely many points. We show that the limit of a sequence of such hypersurfaces always inherits a nontrivial Jacobi field when it has multiplicity one. In a forthcoming paper, we will construct Jacobi fields when the convergence has higher multiplicity. |
Keywords
free boundary minimal surfaces, compactness, Jacobi fields,
curvature estimates
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Mathematical Subject Classification 2010
Primary: 53A10, 53C42
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Milestones
Received: 29 May 2019
Revised: 10 October 2020
Accepted: 5 December 2020
Published: 26 January 2021
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Authors |
| Qiang Guang | |
| Mathematical Sciences
Institute The Australian National University Canberra, ACT Australia |
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| Zhichao Wang | |
| Max-Planck Institute for
Mathematics Bonn Germany |
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| Xin Zhou | |
| Department of Mathematics University of California Santa Barbara Santa Barbara, CA United States |
Department of Mathematics Cornell University Ithaca, NY United States |
