Results 221 to 230 of about 93,932 (267)

Spaces of Harmonic Functions

Journal of the London Mathematical Society, 2000
The paper is mainly concerned with the dimensions of certain spaces of harmonic functions on a complete Riemannian manifold \(M\) of dimension \(n\). It is shown that the study of harmonic functions on \(M\) can be reduced to the study of harmonic functions on each end of \(M\).
Sung, Chiung-Jue, Tam, Luen-Fai, Wang, Jiaping   +2 more
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Harmonic Functions on Manifolds

The Annals of Mathematics, 1997
For an open manifold \(M^n\), given a point \(p\in M^n\), let \(r\) be the distance from \(p\). Define \({\mathcal H}_d(M^n)\) to be the linear space of harmonic functions with order of growth at most \(d\). The main result of this paper is a proof of the following Yau's conjecture: Conjecture. For an open manifold with nonnegative Ricci curvature, the
Colding, Tobias H., Minicozzi, William P. II   +1 more
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Sets of Harmonicity for Finely Harmonic Functions

Potential Analysis, 2004
The author establishes the sharpness of a theorem of Fuglede. \textit{B. Fuglede} [Ann. Inst. Fourier 24, No. 4, 77--91 (1974; Zbl 0287.31003)] observed the following result. Let \(U\) be an open set in \({\mathbb R}^n\) (\(n\geq 2\)). If \(u\) is finely harmonic on \(U\), then there is a dense open subset \(V\) of \(U\) on which \(u\) is harmonic. The
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A Threshold Function for Harmonic Update

SIAM Journal on Discrete Mathematics, 1997
Summary: Harmonic update is a randomized on-line algorithm which, given a random \(m\)-set of vertices \(U(m)\subseteq\{-1,1\}^n\) in the \(n\)-dimensional cube, generates a random vertex \(\mathbf w\in\{-1,1\}^n\) as a putative solution to the system of linear inequalities: \(\sum_{i=1}^n w_i u_i\geq 0\) for each \(\mathbf u\in U(m)\).
Shao C. Fang, Santosh S. Venkatesh
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On a Property of Harmonic Functions

Zeitschrift für Analysis und ihre Anwendungen, 1995
If we divide the space \mathbb R^n into two disjoint areas with one common hypersurface and define a harmonic function in each part of these areas such that their gradients vanish at infinity and the normal components of their gradients are equal on
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On univalent harmonic functions

2002
In Ann. Acad. Sci. Fenn., Ser. A I 9, 3--25 (1984; Zbl 0506.30007) \textit{J. Clunie} and \textit{T. Sheil-Small } introduced and studied the class \(S_H\) of complex valued, harmonic, orientation preserving, univalent functions \(f\) in the unit disk normalized by \(f(0)=0\), \(f'_z(0)-1=0\). Such functions have representation \[ f(z)=h(z)+\overline{g}
Yalçın Tokgöz, Sibel, Öztürk, Metin
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