Results 221 to 230 of about 31,226 (268)

A Report on Harmonic Maps

Bulletin of the London Mathematical Society, 1978
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Eells, James, Lemaire, Luc
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Harmonic maps with potential

Calculus of Variations and Partial Differential Equations, 1997
Let \(f: (M,g)\to (N,h)\) be a smooth map between two Riemannian manifolds and \(G:N\to\mathbb{R}\) be a given function. The authors study the following energy functional \(E_G(f)={1\over 2}\int[|df|^2- 2G(f)]dv_g\), and call \(f\) the harmonic map with potential \(G\) if \(f\) satisfies the Euler-Lagrange equation \(\tau(f)+\nabla G(f)=0\).
FARDOUN A, RATTO, ANDREA
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Harmonic mappings and quasiconformal mappings

Journal d'Analyse Mathématique, 1986
Given a homeomorphism, \(w=H(e^{i\theta})\), \(0\leq \theta \leq 2\pi\), of the unit circumference \(\partial U\), we denote by Q(H) the class of quasiconformal homeomorphisms of U onto itself with boundary values H on \(\partial U\). The extremal dilatation for the class Q(H) is \textit{\(K_ H=\inf \{K[f]:\) \(f\in Q(H)\},\) where \[ K[f]=ess \sup [(|
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On the Conformal Equivalence of Harmonic Maps and Exponentially Harmonic Maps

Bulletin of the London Mathematical Society, 1992
The author considers smooth maps between compact smooth Riemannian manifolds. He pursues the question whether for any given map there exists an exponentially harmonic map that is homotopic to it. He proves that it is true for a manifold modulo a change to a conformally equivalent metric on the preimage manifold and dimension greater than or equal to 3.
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On Convolution of Harmonic Mappings

Complex Analysis and Operator Theory, 2020
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Another Report on Harmonic Maps

Bulletin of the London Mathematical Society, 1988
Ten years ago the authors of the paper gave an interesting account of the theory of harmonic maps in their paper [Bull. Lond. Math. Soc. 10, 1-68 (1978; Zbl 0401.58003)] where they presented the most important results known at that time. In the present paper the authors give a survey of the progress made during the past decade.
Eells, James, Lemaire, Luc
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On Homotopic Harmonic Maps

Canadian Journal of Mathematics, 1967
Let M, M′ be C∞ Riemann manifolds such that(1.0) M is compact;(1.1) M′ is complete and its sectional curvatures are non-positive.In terms of local coordinates x = (x1, … , xn) on M and y = (y1, … , ym) on M′, let the respective Riemann elements of arc-length beand Γijk, Γ′αβγ be the corresponding Christoffel symbols.
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Neighborhoods of Harmonic and Stable Harmonic Mappings

Bulletin of the Malaysian Mathematical Sciences Society
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Bappaditya Bhowmik, Santana Majee
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Harmonic maps and harmonic morphisms

Journal of Mathematical Sciences, 1999
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Properties of the mappings that are close to the harmonic mappings

Siberian Mathematical Journal, 1998
This a continuation of the author's paper [Sib. Math. J. 39, No. 4, 765-780 (1998; Zbl 0915.30019)]. The results of the article include a theorem on the connection between the notion of \(\varepsilon\)-quasiharmonic mapping and the solutions to Beltrami systems, an analog to the arithmetic mean property of harmonic functions for \(\varepsilon ...
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