The qualitative behavior for biharmonic functions on open manifolds

2025/11/12 by Wang, Lin, Zhu, Miaomiao · 2 citations
#31A30 #58J05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.09393

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 ℝⁿ satisfying certain coefficient conditions.

Cited by

• Ancient Solutions to the Biharmonic Heat Equation
• A Polyharmonic Liouville Hierarchy on Complete Manifolds of Nonnegative Ricci Curvature

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