We show that under certain symmetry, the images of complete harmonic embeddings from the complex plane into the hyperbolic plane is completely determined by the geometric information of the vertical measured foliation and is independent of the horizontal measured foliation of the corresponding Hopf differentials. In this paper, we find a new explicit relation between the image of harmonic embed...

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with locally doubling measure supporting local $p$-Poincar\'e inequality. Similar classifications have earlier been obtained Riemann surfaces Riemannian manifolds. We also study the inclusions between these classes o...

We generalize the notion of cusp excursion geodesic rays by introducing for any \begin{document}$ k\geq 1 $\end{document} \begin{document}$ k^\text{th} excursion in cusps a hyperbolic id="M3">\begin{document}$ N $\end{document}-manifol...

Brain Cortical surface registration is required for inter-subject studies of functional and anatomical data. Harmonic mapping has been applied for brain mapping, due to its existence, uniqueness, regularity and numerical stability. In order to improve the registration accuracy, sculcal landmarks are usually used as constraints for brain registration. Unfortunately, constrained harmonic mappings...

in this paper, a new t-s fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. fuzzy controller is designed based on the parallel distributed compensation (pdc), and with a new lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived v...

The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of along illustrated. numerical algorithm provided based collocation method and Tikhonov regularization. estimates parabolic hyperbolic are demonstrated by examples respectively.

We study harmonic maps from a 3-manifold with boundary to $$\mathbb {S}^1$$ and prove special case of Gromov dihedral rigidity three-dimensional cubes whose angles are $$\pi / 2$$ . Furthermore, we give some applications mapping torus hyperbolic 3-manifolds.

The potential function of Lippincott and Schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. The parameters originally introduced to the potential function by Lippincott and Schroeder have been determined from the structural parameters such as 0.. .Odistance 0-H bond distance, H.. .O distance and HOO angle. Thevalidity of harmonic oscillator appr...