# $(n,\rho)-$harmonic mappings and energy minimal deformations between annuli

## TL;DR

This paper extends previous work on energy-minimizing Sobolev homeomorphisms between annuli in Euclidean space, solving a minimization problem involving radial metrics and harmonic mappings, contributing to the Nitsche conjecture.

## Contribution

It generalizes earlier results by solving the $(
ho,n)$ energy minimization problem for Sobolev homeomorphisms between concentric annuli, using solutions to Euler-Lagrange equations for radial harmonic maps.

## Key findings

- Solved the $(
ho,n)$ energy minimization problem for Sobolev homeomorphisms.
- Extended results to higher dimensions and general radial metrics.
- Provided new insights into the Nitsche conjecture.

## Abstract

We extend the main results obtained by Iwaniec and Onninen in Memoirs of the AMS (2012). In the paper it is solved the minimization problem of $(\rho,n)$ energy of Sobolev homeomorphisms between two concentric annuli in the Euclidean space $\mathbf{R}^n$. Here $\rho$ is a radial metric defined in the image annulus. The key of the proofs comes from the solution to the Euler-Lagrange equation for radial harmonic mapping. This is a new contribution on the topic of famous Nitsche conjecture.