A note on equivariant biharmonic maps and stable biharmonic maps

@article{Ou2020ANO,
  title={A note on equivariant biharmonic maps and stable biharmonic maps},
  author={Ye-Lin Ou},
  journal={Journal of Mathematical Analysis and Applications},
  year={2020}
}
  • Ye-Lin Ou
  • Published 7 October 2019
  • Mathematics
  • Journal of Mathematical Analysis and Applications
Stability and the index of biharmonic hypersurfaces in a Riemannian manifold
  • Ye-Lin Ou
  • Mathematics
    Annali di Matematica Pura ed Applicata (1923 -)
  • 2021
In this paper, we give an explicit second variation formula for a biharmonic hypersurface in a Riamannian manifold similar to that of a minimal hypersurface. We then use the second variation formula
On p-biharmonic curves
TLDR
By making a connection to magnetic geodesic the authors are able to prove the existence of 12 -biharmonic curves on closed surfaces and classify 12 -elastic curves onclosed surfaces and three-dimensional space forms making use of the results obtained for 12 -Elastic curves from the literature.

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Stability and the index of biharmonic hypersurfaces in a Riemannian manifold
  • Ye-Lin Ou
  • Mathematics
    Annali di Matematica Pura ed Applicata (1923 -)
  • 2021
In this paper, we give an explicit second variation formula for a biharmonic hypersurface in a Riamannian manifold similar to that of a minimal hypersurface. We then use the second variation formula
Biharmonic Conformal Maps in Dimension Four and Equations of Yamabe-Type
We prove that the problem of constructing biharmonic conformal maps on a 4-dimensional Einstein manifold reduces to a Yamabe-type equation. This allows us to construct an infinite family of examples
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This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant
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In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute
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In recent years, the study of the bienergy functional has attracted the attention of a large community of researchers, but there are not many examples where the second variation of this functional
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In this paper, λ -harmonic maps from a Finsler manifold to a Riemannian manifold are studied. Then, some properties of this kind of harmonic maps are presented and some examples are given. Finally,
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