Embedded tori with prescribed mean curvature

Paolo Caldiroli, Monica Musso

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)
29 Downloads (Pure)


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
Early online date16 Oct 2018
Publication statusPublished - 15 Dec 2018


  • Prescribed mean curvature
  • Unduloids

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Embedded tori with prescribed mean curvature'. Together they form a unique fingerprint.

Cite this