Finite-dimensionality conjecture for bounded biharmonic functions on manifolds with nonnegative Ricci curvature
Finite-dimensionality conjecture for bounded biharmonic functions on manifolds with nonnegative Ricci curvature
Let be an open manifold with nonnegative Ricci curvature, and let be a bounded biharmonic function on , meaning that in the source's terminology via the biharmonic equation . Bounded biharmonic-function conjecture. Every bounded biharmonic function on is constant. The source presents this as a natural conjecture because bounded biharmonic functions can be nonconstant on some complete noncompact manifolds, while the resolution status is not specified.
Sources & referencesView supporting material
Primary source
Lin Wang and Miaomiao Zhu, “The qualitative behavior for biharmonic functions on open manifolds”, arXiv:2511.09393 (2025).
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