Ambrozio, L, Buzano, R, Carlotto, A et al. (1 more author) (2022) Geometric convergence results for closed minimal surfaces via bubbling analysis. Calculus of Variations and Partial Differential Equations, 61 (1). 25. ISSN 0944-2669
Abstract
We present some geometric applications, of global character, of the bubbling analysis developed by Buzano and Sharp for closed minimal surfaces, obtaining smooth multiplicity one convergence results under upper bounds on the Morse index and suitable lower bounds on either the genus or the area. For instance, we show that given any Riemannian metric of positive scalar curvature on the three-dimensional sphere the class of embedded minimal surfaces of index one and genus γ is sequentially compact for any γ≥1. Furthemore, we give a quantitative description of how the genus drops as a sequence of minimal surfaces converges smoothly, with mutiplicity m≥1, away from finitely many points where curvature concentration may happen. This result exploits a sharp estimate on the multiplicity of convergence in terms of the number of ends of the bubbles that appear in the process.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2021. This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) |
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: | 13 Oct 2021 13:40 |
Last Modified: | 25 Jun 2023 22:47 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00526-021-02135-x |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:179086 |
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