Harmonicity of horizontally conformal maps and spectrum of the Laplacian.
Yun, Gabjin (2002)
International Journal of Mathematics and Mathematical Sciences
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Yun, Gabjin (2002)
International Journal of Mathematics and Mathematical Sciences
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A. Mohammed Cherif, Djaa Mustapha (2014)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we study the characterization of generalized -harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an -harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144],...
John B. Walsh (1977)
Séminaire de probabilités de Strasbourg
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Hélein, Frédéric (1998)
Documenta Mathematica
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Adam Osękowski (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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Assume that u, v are conjugate harmonic functions on the unit disc of ℂ, normalized so that u(0) = v(0) = 0. Let u*, |v|* stand for the one- and two-sided Brownian maxima of u and v, respectively. The paper contains the proof of the sharp weak-type estimate ℙ(|v|* ≥ 1)≤ (1 + 1/3² + 1/5² + 1/7² + ...)/(1 - 1/3² + 1/5² - 1/7² + ...) 𝔼u*. Actually, this estimate is shown to be true in the more general setting of differentially subordinate harmonic functions...
R.K. Getoor, M.J. Sharpe (1972)
Inventiones mathematicae
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Anderson, G.D., Lehtinen, M., Vuorinen, M. (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Bent Fuglede (1978)
Annales de l'institut Fourier
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A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, 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 vanishes. Every non-constant harmonic morphism is shown to be...
Ou, Ye-Lin, Wei, Shihshu Walter (2004)
Beiträge zur Algebra und Geometrie
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B. Johnson (1973)
Studia Mathematica
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