Pluripolarity of manifolds

TL;DR

This paper extends classical pluripolarity results from real-analytic manifolds to those of the Gevrey class, generalizing recent findings on pluripolarity of Gevrey class curves.

Contribution

It generalizes the pluripolarity of non-generic manifolds from real-analytic to Gevrey class manifolds, broadening the scope of previous results.

Findings

Gevrey class manifolds are pluripolar under certain conditions

Extension of Bedford's classical result to Gevrey manifolds

Generalization of pluripolarity of curves in Gevrey class

Abstract

By the classical result of E. Bedford, a real-analytic non-generic manifold is pluripolar. We extend this result for manifolds of the Gevrey class. This also gives a generalization of the recent result of D. Coman, N. Levenberg and E. Poletsky on pluripolarity of curves of the Gevrey class.