Extremal metrics for Laplace eigenvalues in perturbed conformal classes
arXiv:1608.06829
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.
There is a gap in the proof of Theorem 1.11. There will be two shorter papers containing the remaining results soon