Displaying similar documents to “Harmonic Functions of Polynomial Growth on Certain Complete Manifolds.”

A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

Ricardo Costa, Gaspar J. Machado, Stéphane Clain (2015)

International Journal of Applied Mathematics and Computer Science

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A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the...

Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

Annales de l'institut Fourier

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A harmonic morphism f : M N between Riemannian manifolds M and N is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim M dim N , since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where d f vanishes. Every non-constant harmonic morphism is shown to be...