The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3892–3905 | Cite as

Biharmonic Conformal Maps in Dimension Four and Equations of Yamabe-Type

  • Paul BairdEmail author
  • Ye-Lin Ou


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 on the Euclidean 4-sphere. In addition, we characterize all solutions on Euclidean 4-space and show that there exists at least one proper biharmonic conformal map from any closed Einstein 4-manifold of negative Ricci curvature.


Biharmonic map Conformal biharmonic map Einstein 4-manifold Yamabe equation Möbius transformation 

Mathematics Subject Classification

58E20 53A30 


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Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de Bretagne Atlantique UMR 6205Université de Bretagne OccidentaleBrest Cedex 3France
  2. 2.Department of MathematicsTexas A & M University-CommerceCommerceUSA

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