Bellettini, Costante;
Workman, Myles;
(2024)
Embeddedness of Min-Max CMC Hypersurfaces in
Manifolds with Positive Ricci Curvature.
Nonlinear Differential Equations and Applications: NoDEA
, 31
, Article 27. 10.1007/s00030-023-00910-7.
(In press).
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Abstract
We prove that on a compact Riemannian manifold of dimension 3 or higher, with positive Ricci curvature, the Allen–Cahn min–max scheme in Bellettini and Wickramasekera (The Inhomogeneous Allen– Cahn Equation and the Existence of Prescribed-Mean-Curvature Hypersurfaces, 2020), with prescribing function taken to be a non-zero constant λ, produces an embedded hypersurface of constant mean curvature λ (λCMC). More precisely, we prove that the interface arising from said min– max contains no even-multiplicity minimal hypersurface and no quasiembedded points (both of these occurrences are in principle possible in the conclusions of Bellettini and Wickramasekera, 2020). The immediate geometric corollary is the existence (in ambient manifolds as above) of embedded, closed λ-CMC hypersurfaces (with Morse index 1) for any prescribed non-zero constant λ, with the expected singular set when the ambient dimension is 8 or higher
| Type: | Article |
|---|---|
| Title: | Embeddedness of Min-Max CMC Hypersurfaces in Manifolds with Positive Ricci Curvature |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00030-023-00910-7 |
| Publisher version: | https://doi.org/10.1007/s00030-023-00910-7 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10182251 |
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