Results 11 to 20 of about 36,653 (283)
On harmonic entire mappings [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 In this paper, we investigate properties of harmonic entire mappings. Firstly, we give the characterizations of the order and the type for a harmonic entire mapping $f=h+\overline{g}$, respectively, and also consider the relationship between the order and the type of $f$, $h$, and $g$.
Hua Deng +3 more
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Rosette Harmonic Mappings [PDF]
Complex Analysis and Operator Theory, 2021 A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These mappings are analogous to the $n$-cusped hypocycloid, but are modified by Gauss hypergeometric factors, both in the ...
Jane McDougall, Lauren Stierman
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Communications in Information and Systems, 2003 We develop two different techniques to study volume mapping problem in Computer Graphics and Medical Imaging fields. The first one is to find a harmonic map from a 3 manifold to a 3D solid sphere and the second is a sphere carving algorithm which calculates the simplicial decomposition of volume adapted to surfaces.
Wang , Yalin +2 more
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Monopoles and harmonic maps [PDF]
Journal of Mathematical Physics, 1999 Recently Jarvis has proved a correspondence between SU(N) monopoles and rational maps of the Riemann sphere into flag manifolds. Furthermore, he has outlined a construction to obtain the monopole fields from the rational map. In this paper we examine this construction in some detail and provide explicit examples for spherically symmetric SU(N ...
Ioannidou, Theodora, Sutcliffe, Paul M.
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Pacific Journal of Mathematics, 1989 A construction is given whereby a Riemannian manifold induces a Riemannian metric on the total space of a large class of fibre bundles over it. Using this metric on the appropriate bundles, necessary and sufficient conditions are given for the Gauss map and the spherical Gauss map to be harmonic.
Jensen, Gary R., Rigoli, Marco
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Univalent harmonic mappings [PDF]
Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1996 Summary: A family of univalent harmonic functions is studied from the point of geometric function theory. This class consists of mappings of the open unit disk onto the entire complex plane except for two infinite slits along the real axis with a normalization at the origin.
Öztürk, Metin, Yamankaradeniz, Mümin
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Convergence of Harmonic Maps [PDF]
The Journal of Geometric Analysis, 2015 In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
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Harmonic Mappings of Spheres [PDF]
American Journal of Mathematics, 1972 This thesis is addressed to the following fundamental problem: given a homotopy class of maps between compact Riemannian manifolds N and M, is there a harmonic representative of that class? Eells and Sampson have given a general existence theorem for the case that M has no positive sectional curvatures [ESJ.\ud Otherwise, very little is known ...
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Harmonic Maps and Biharmonic Maps [PDF]
Symmetry, 2015 This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.
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Limits of $\alpha$-harmonic maps [PDF]
Journal of Differential Geometry, 2020 Critical points of approximations of the Dirichlet energy \`{a} la Sacks-Uhlenbeck are known to converge to harmonic maps in a suitable sense. However, we show that not every harmonic map can be approximated by critical points of such perturbed energies. Indeed, we prove that constant maps and the rotations of $S^2$ are the only critical points of $E_{\
Tobias Lamm +2 more
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