Spherical harmonics generating bounded biharmonics
Authors: Bradley Beaver, Leo Sario and Cecilia Wang
Journal: Proc. Amer. Math. Soc. 84 (1982), 485-491
MSC: Primary 31C12; Secondary 31A30, 31B30
MathSciNet review: 643735
Abstract: Let be the family of bounded nonharmonic biharmonic functions on a Riemannian manifold . On the punctured Euclidean -space , is void for , whereas for , it is generated by certain fundamental spherical harmonics. It is also known that remains void on the Riemannian manifold , , obtained by endowing with the non-Euclidean metric , .
The purpose of the present paper is to show that the fundamental spherical harmonics continue generating , despite the distorting metric . An analogous result holds for .
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