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arXiv · 2511.09393

The qualitative behavior for biharmonic functions on open manifolds

Lin Wang·Miaomiao Zhu
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Abstract

For a complete noncompact Riemannian manifold with nonnegative Ricci curvature, we show that bounded biharmonic functions are constant and the space consists of biharmonic functions with polynomial growth of a fixed rate is finite dimensional. Also, we derive a Weyl type bound for this space. Finally, we present a finite dimensional result for a class of fourth-order operators on $\mathbb{R}^n$ satisfying certain coefficient conditions.

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Lin Wang, Miaomiao Zhu. 2025-11-12. The qualitative behavior for biharmonic functions on open manifolds. https://arxiv.org/abs/2511.09393

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