English

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.

Keywords

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

R2 v1 2026-06-22T15:29:18.383Z