Results 1 to 10 of about 149 (148)
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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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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Globally diffeomorphic $$\sigma$$-harmonic mappings [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2020 AbstractGiven a two-dimensional mapping U whose components solve a divergence structure elliptic equation, we give necessary and sufficient conditions on the boundary so that U is a global diffeomorphism.
Alessandrini G., Nesi V.
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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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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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Analysis, 2009 We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These maps are called affine harmonic.
Şimşir, Fatma Muazzez, Jost J.
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Proceedings of the American Mathematical Society, 1958 1. Suppose that the functions x=x(a, 3), y=y(a, f) define a oneto-one harmonic mapping of the unit disc P in the a, p3-plane (a+i3 ==y) onto a convex domain C in the x, y-plane (x+iy=z). The origin is assumed to be fixed. Introducing two functions F(y) and G(y) which, in r, depend analytically upon the variable y we may write z = Re F(,y) +i Re G(y ...
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Nagoya Mathematical Journal, 2019 We develop the notion of renormalized energy in Cauchy–Riemann (CR) geometry for maps from a strictly pseudoconvex pseudo-Hermitian manifold to a Riemannian manifold. This energy is a CR invariant functional whose critical points, which we call CR-harmonic maps, satisfy a CR covariant partial differential equation. The corresponding operator coincides
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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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