Compactness of isospectral conformal Finslerian metrics set on a 3manifold
Abstract
Let F be a Finslerian metric on an ndimensional closed manifold M. In this work, we study problems about compactness of isospectral sets of conformal Finslerian metrics when n=3. More precisely, let $\widetilde{F}\in[F]$ be a Finslerian metric in the conformal class of $F$ whose scalar curvature is nonpositive constant. We show that the set of metrics in $[F]$ isospectral to $\widetilde{F}$ is compact in the $C^{\infty}$topology.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2110.06338
 Bibcode:
 2021arXiv211006338N
 Keywords:

 Mathematics  General Mathematics