Ambrozio, L, Buzano, R, Carlotto, A et al. (1 more author) (2019) Bubbling analysis and geometric convergence results for free boundary minimal surfaces. Journal de l'École polytechnique — Mathématiques, 6. pp. 621-664. ISSN 2429-7100
Abstract
We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points where curvature concentration occurs. Thereby, we derive a general quantization identity for the total curvature functional, valid in ambient dimension less than eight and applicable to possibly improper limit hypersurfaces. In dimension three, this identity can be combined with the Gauss-Bonnet theorem to provide a constraint relating the topology of the free boundary minimal surfaces in a converging sequence, of their limit, and of the bubbles or half-bubbles that occur as blow-up models. We present various geometric applications of these tools, including a description of the behaviour of index one free boundary minimal surfaces inside a 3-manifold of non-negative scalar curvature and strictly mean convex boundary. In particular, in the case of compact, simply connected, strictly mean convex domains in R3 unconditional convergence occurs for all topological types except the disk and the annulus, and in those cases the possible degenerations are classified.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The authors, 2019. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Surfaces minimales à bord libre; analyse des bulles; quantification; compacité géométrique |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Nov 2019 14:15 |
Last Modified: | 25 Jun 2023 22:03 |
Status: | Published |
Publisher: | Ecole Polytechnique |
Identification Number: | 10.5802/jep.102 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:153612 |