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

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

2010-01-28

arxiv.org/abs/1001.5231v1

Manuscripta Math. 133 (2010), 115-130

Mathematics

Analysis of PDEs

15 Pages

Scientific paper

10.1007/s00229-010-0365-1

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

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