First eigenvalues of free boundary hypersurfaces in the unit ball along the inverse mean curvature flow

Abstract

In this note, we consider the first nonzero eigenvalue λp,1 of the p-Laplacian on free boundary proper hypersurfaces in the unit ball evolving along the inverse mean curvature flow. We show that λp,1 is monotone decreasing along the flow. Using the convergence of free boundary disks in the unit ball, we give a lower bound of λp,1 of a free boundary disk type hypersurface in the unit ball.