Extremal metrics for Laplace eigenvalues in perturbed conformal classes
Differential Geometry
2016-12-16 v3 Analysis of PDEs
Abstract
We prove that in many cases the existence of an extremal metric for some Laplace eigenvalue in a conformal class allows to find extremal metrics in conformal classes close by. As a consequence and as part of the arguments we obtain perturbed harmonic maps with constant density.
Cite
@article{arxiv.1608.06829,
title = {Extremal metrics for Laplace eigenvalues in perturbed conformal classes},
author = {Henrik Matthiesen},
journal= {arXiv preprint arXiv:1608.06829},
year = {2016}
}
Comments
There is a gap in the proof of Theorem 1.11. There will be two shorter papers containing the remaining results soon