Displaying similar documents to “Growth and asymptotic sets of subharmonic functions (II)”

Unbounded harmonic functions on homogeneous manifolds of negative curvature

Richard Penney, Roman Urban (2002)

Colloquium Mathematicae

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We study unbounded harmonic functions for a second order differential operator on a homogeneous manifold of negative curvature which is a semidirect product of a nilpotent Lie group N and A = ℝ⁺. We prove that if F is harmonic and satisfies some growth condition then F has an asymptotic expansion as a → 0 with coefficients from 𝓓'(N). Then we single out a set of at most two of these coefficients which determine F. Then using asymptotic expansions we are able to prove...

A remark on gradients of harmonic functions.

Wen Sheng Wang (1995)

Revista Matemática Iberoamericana

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In any C domain, there is nonzero harmonic function C continuous up to the boundary such that the function and its gradient on the boundary vanish on a set of positive measure.