Nonlinear Analysis and Geometric Function Theory

Ljubomir B Ćirić,Qamrul Hasan Ansari,Samuel Krushkal,David Kalaj,Vesna Manojlović

doi:10.1155/2014/656957

Abstract

1 Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia 2Department of Mathematics, Bar-Ilan University, 5290002 Ramat-Gan, Israel 3 Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India 4 Faculty of Natural Sciences and Mathematics, University of Montenegro, 81000 Podgorica, Montenegro 5Mathematical Institute SANU and Faculty of Organizational Sciences, University of Belgrade, 11000 Belgrade, Serbia

Highlights

Quasiconformal mappings, or deformations, between subsets of Euclidean space or manifolds and harmonic maps between manifolds, may arise as the solutions to certain optimization problems in the calculus of variations, as stationary points which are the solutions to differential equations
The most recent developments in the theory of planar and space quasiconformal mappings are related to the theory to degenerate elliptic equations, which include p-Laplace equation whose solutions are p-harmonic maps
Harmonic maps have played a role in compactifications and parametrizations of Teichmuller space, via classical results of Mike Wolf, who gave a compactification in terms of hyperbolic harmonic maps

Summary

Introduction

In connection with the general trend of the geometric function theory in Euclidean space to generalize certain aspects of the analytic functions of one complex variable, there is another development related to maps of quasiconformal type, which are solutions of nonlinear secondorder elliptic equations or satisfy certain inequality related to Laplacian and gradient. Editorial Nonlinear Analysis and Geometric Function Theory SiriT,1 Samuel Krushkal,2 Qamrul Hasan Ansari,3 David Kalaj,4 and Vesna ManojloviT5

Results

Conclusion