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Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature
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Ikoma, Norihisa, Malchiodi, Andrea and Mondino, Andrea (2019) Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature. International Mathematics Research Notices, 2020 (19). pp. 6539-6568. doi:10.1093/imrn/rny203 ISSN 1073-7928.
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Official URL: https://doi.org/10.1093/imrn/rny203
Abstract
Let (M,g) be a three-dimensional Riemannian manifold. The goal of the paper is to show that if P0∈M is a nondegenerate critical point of the scalar curvature, then a neighborhood of P0 is foliated by area-constrained Willmore spheres. Such a foliation is unique among foliations by area-constrained Willmore spheres having Willmore energy less than 32π; moreover, it is regular in the sense that a suitable rescaling smoothly converges to a round sphere in the Euclidean three-dimensional space. We also establish generic multiplicity of foliations and the 1st multiplicity result for area-constrained Willmore spheres with prescribed (small) area in a closed Riemannian manifold. The topic has strict links with the Hawking mass.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Foliations (Mathematics), Sphere, Curvature | |||||||||
| Journal or Publication Title: | International Mathematics Research Notices | |||||||||
| Publisher: | Oxford University Press | |||||||||
| ISSN: | 1073-7928 | |||||||||
| Official Date: | October 2019 | |||||||||
| Dates: |
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| Volume: | 2020 | |||||||||
| Number: | 19 | |||||||||
| Page Range: | pp. 6539-6568 | |||||||||
| DOI: | 10.1093/imrn/rny203 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record [insert complete citation information here] is available online at:Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino; Foliation by Area-constrained Willmore Spheres Near a Nondegenerate Critical Point of the Scalar Curvature, International Mathematics Research Notices, , rny203, https://doi.org/10.1093/imrn/rny203 | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| Date of first compliant deposit: | 15 August 2018 | |||||||||
| Date of first compliant Open Access: | 31 August 2019 | |||||||||
| RIOXX Funder/Project Grant: |
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