A global pinching theorem for surfaces with constant mean curvature in S3

Yi-Jung Hsu*, Tai Ho Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let M be a compact immersed surface in the unit sphere S3 with constant mean curvature H. Denote by φ the linear map from Tp(M) into Tp(M), φ = A - H/2 I, where A is the linear map associated to the second fundamental form and I is the identity map. Let φ denote the square of the length of φ. We prove that if ∥φ∥L(2) ≤ C, then M is either totally umbilical or an H(r)-torus, where C is a constant depending only on the mean curvature H.

Original languageEnglish
Pages (from-to)157-161
Number of pages5
JournalProceedings of the American Mathematical Society
Volume130
Issue number1
DOIs
StatePublished - 1 Jan 2002

Keywords

  • Mean curvature
  • Sphere
  • Totally umbilical

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