Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature

Norihisa Ikoma, Andrea Malchiodi, Andrea Mondino

Research output: Contribution to journalArticlepeer-review

Abstract

Let (M, g) be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if P0∈ M is a non-degenerate 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 first 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
JournalUnknown Journal
Publication statusPublished - 2018 Jun 1

Keywords

  • Foliation
  • Hawking mass
  • Lyapunov-Schmidt reduction
  • Nonlinear fourth order partial differential equations
  • Willmore functional

ASJC Scopus subject areas

  • General

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