# Existence of solutions to a higher dimensional mean-field equation on manifolds

created by martinazz on 29 Jan 2010
modified on 17 Jul 2018

[BibTeX]

Accepted Paper

Inserted: 29 jan 2010
Last Updated: 17 jul 2018

Journal: Manuscripta Math.
Year: 2010

ArXiv: 1001.5231 PDF
Notes:

15 pages

Abstract:

For $m\geq 1$ we prove an existence result for the equation $$(-\Deltag)m u+\lambda=\lambda\frac{e{2mu}}{\intM e{2mu}d\mug}$$ on a closed Riemannian manifold $(M,g)$ of dimension $2m$ for certain values of $\lambda$.