Intrinsically biharmonic maps into homogeneous spaces

Peter Hornung, Roger Moser

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The tension field $\tau(u)$ of a map $u$ from a domain ­ $\Omega \subset \mathbb{R}^m$ into a manifold $N$ is the negative $L^2$-gradient of the Dirichlet energy. In this paper we study critical points of the intrinsic biharmonic energy functional $T(u) = \int_\Omega |\tau(u)|^2$ when $N$ is a homogeneous space. We derive an Euler-Lagrange equation which makes sense for all critical points of $T$, in contrast to previously known versions. We also obtain a partial regularity result for solutions to this equation for arbitrary domain dimension.
Original languageEnglish
Pages (from-to)411–425
JournalAdvances in Calculus of Variations
Volume5
Issue number4
DOIs
Publication statusPublished - 2012

Fingerprint Dive into the research topics of 'Intrinsically biharmonic maps into homogeneous spaces'. Together they form a unique fingerprint.

  • Projects

  • Cite this