Willmore-type energies and willmore-type surfaces in space forms

Bhagya Athukorallage, Giorgio Bornia, Thanuja Paragoda, Magdalena Toda

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The current report studies Willmore-type energies and Willmore-type immersions in space forms. First, we introduce the notion of deformed Willmore energy for a space form as such that the constants are independent. Next, we discuss the corresponding Euler-Lagrange equation for the deformed energy. This approach provides a natural justification to Willmore’s definition of the appropriate Willmore-type energy in a space form We deduce the Euler-Lagrange equation of the deformed Willmore energy in a space form, in a unified way, using an extrinsic Laplace-Beltrami operator (which depends on both the surface metric and the ambient space form). We consider both the case of closed surfaces and one of surfaces with boundary, for which we gave and discussed the necessary boundary value conditions, where the previous literature failed to do. Thus, we show that our work provides a bridge between prior works in the field, as well as a novel approach.

Original languageEnglish
Pages (from-to)93-108
Number of pages16
JournalJP Journal of Geometry and Topology
Volume18
Issue number2
DOIs
StatePublished - Nov 2015

Keywords

  • Deformed Willmore energy
  • Minimal surface
  • Space form
  • Willmore energy
  • Willmore surface

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