Q-Type Spaces of Harmonic Mappings by Alaa Kamal

“…In this paper, we attempt to investigate a new harmonic mapping class denoted by the Banach space QHp in the unit disk. …”
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On Convolution and Convex Combination of Harmonic Mappings by Ahmad Sulaiman Ahmad El-Faqeer, Zhen Chuan Ng, Shamani Supramaniam

“…Furthermore, convolutions of two special subclasses of univalent harmonic mappings are shown to be convex in the horizontal direction. …”
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Conservation law of harmonic mappings in supercritical dimensions by Guo, Chang-Yu, Xiang, Chang-Lin

“…As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.…”
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Composition Operators on Some Banach Spaces of Harmonic Mappings by Munirah Aljuaid, Flavia Colonna

“…We study the composition operators on Banach spaces of harmonic mappings that extend several well-known Banach spaces of analytic functions on the open unit disk in the complex plane, including the α-Bloch spaces, the growth spaces, the Zygmund space, the analytic Besov spaces, and the space BMOA.…”
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A Schwarz lemma of harmonic maps into metric spaces by Jie Wang

Subjects: “…harmonic maps…”
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Normality of the p-Harmonic and Log-p-Harmonic Mappings by Qinghua Jiang, Fanning Meng, Guoqiang Dang

“…In this paper, the concepts of p-harmonic mappings and log-p-harmonic mappings in the unit disk have been introduced and studied by many researchers. …”
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A Family of Minimal Surfaces and Univalent Planar Harmonic Mappings by Michael Dorff, Stacey Muir

“…We present a two-parameter family of minimal surfaces constructed by lifting a family of planar harmonic mappings. In the process, we use the Clunie and Sheil-Small shear construction for planar harmonic mappings convex in one direction. …”
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General Approach to Regions of Variability via Subordination of Harmonic Mappings by Sh. Chen, S. Ponnusamy, X. Wang

“…Using subordination, we determine the regions of variability of several subclasses of harmonic mappings. We also graphically illustrate the regions of variability for several sets of parameters for certain special cases.…”
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Twistor fibrations giving primitive harmonic maps of finite type by Rui Pacheco

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Continuous in time bubble decomposition for the harmonic map heat flow by Jacek Jendrej, Andrew Lawrie, Wilhelm Schlag

“…We consider the harmonic map heat flow for maps $\mathbb {R}^{2} \to \mathbb {S}^2$ . …”
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The Morse Index of Sacks–Uhlenbeck α-Harmonic Maps for Riemannian Manifolds by Amir Shahnavaz, Nader Kouhestani, Seyed Mehdi Kazemi Torbaghan

“…In this paper, first we prove a nonexistence theorem for α-harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α-harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. …”
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Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings by Sh. Chen, S. Ponnusamy, X. Wang

“…We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. …”
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Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere by Detaille, Antoine, Mazowiecka, Katarzyna

Subjects: “…Harmonic maps…”
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Almost contact metric 3-submersions by Bill Watson

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Pluriharmonic Mappings with the Convex Holomorphic Part by Ma Lihua, See Keong Lee

“…In 2018, Partyka et al. established several equivalent conditions for a sense-preserving locally injective harmonic mapping f=h+g¯ in the unit disk D with convex holomorphic part h to be quasiconformal in terms of the relationships of two-point distortion of h, g, and f. …”
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The Properties of a New Subclass of Harmonic Univalent Mappings by Zhi-Hong Liu, Ying-Chun Li

“…First, we showed that the convolutions of two special subclass harmonic mappings are convex in the horizontal direction. …”
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Local solvability of a constrainedgradient system of total variation by Yoshikazu Giga, Yohei Kashima, Noriaki Yamazaki

“…A 1-harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in ℝN, is formulated by the use of subdifferentials of a singular energythe total variation. …”
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Harmonic Subtangent Structures by Adara M. Blaga

“…Conditions for a subtangent harmonic structure to be preserved by harmonic maps are also given.…”
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Construction of Planar Harmonic Functions by Jay M. Jahangiri, Herb Silverman, Evelyn M. Silvia

“…In this paper, we construct certain planar harmonic maps either by varying the coanalytic parts of harmonic functions that are known to be harmonic starlike or by adjoining analytic univalent functions with coanalytic parts that are related or derived from the analytic parts.…”
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