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arXiv · 1707.03326

Biharmonic conformal maps in dimension four and equations of Yamabe-type

Paul Baird·Ye-Lin Ou
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Abstract

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 non-constant proper biharmonic conformal map from any closed Einstein 4-manifold of negative Ricci curvature.

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Paul Baird, Ye-Lin Ou. 2017-07-11. Biharmonic conformal maps in dimension four and equations of Yamabe-type. https://arxiv.org/abs/1707.03326

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