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Roadmap on singular optics and its applications. [PDF]
Balasubramaniam GM +49 more
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Large language models for intelligent RDF knowledge graph construction: results from medical ontology mapping. [PDF]
Mavridis A +4 more
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Fault Diagnosis of Rotating Machinery Using Supervised Machine Learning Algorithms with Integrated Data-Driven and Physics-Informed Feature Sets. [PDF]
Ignjatovska AA +6 more
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Bulletin of the London Mathematical Society, 1978
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Eells, James, Lemaire, Luc
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Eells, James, Lemaire, Luc
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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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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, 1986Given 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, 1992The 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, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Another Report on Harmonic Maps
Bulletin of the London Mathematical Society, 1988Ten 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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