Embedded tori with prescribed mean curvature

Paolo Caldiroli, Monica Musso

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
20 Downloads (Pure)

Abstract

We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form H(X)=1+A|X| −γ for |X| large, when A<0 and γ∈(0,2). Such surfaces are close to sections of unduloids with small neck-size, folded along circumferences centered at the origin and with larger and larger radii. The construction involves a deep study of the corresponding Jacobi operators, an application of the Lyapunov–Schmidt reduction method and some variational argument.

Original languageEnglish
Pages (from-to)406-458
Number of pages53
JournalAdvances in Mathematics
Volume340
Early online date16 Oct 2018
DOIs
Publication statusPublished - 15 Dec 2018

Keywords

  • Prescribed mean curvature
  • Unduloids

ASJC Scopus subject areas

  • Mathematics(all)

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