Foliation by area-constrained willmore spheres near a nondegenerate critical point of the scalar curvature

Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)6539-6568
Number of pages30
JournalInternational Mathematics Research Notices
Volume2020
Issue number19
DOIs
Publication statusPublished - 2021

ASJC Scopus subject areas

  • Mathematics(all)

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