Evolution of eigenvalue of the Wentzell–Laplace operator along the conformal mean curvature flow

In this paper, we investigate continuity, differentiability and monotonicity for the first nonzero eigenvalue of the Wentzell–Laplace operator along the conformal mean curvature flow on $n$-dimensional compact manifolds with boundary for $n \geq 3$ under a boundary condition. In especial, we show that the first nonzero eigenvalue of the Wentzell–Laplace operator is monotonic under the conformal mean curvature flow and we find some monotonic quantities dependent to the first nonzero eigenvalue along the conformal mean curvature flow.

Keywords

eigenvalues, Wentzell–Laplace operator, mean curvature flow, conformal

2010 Mathematics Subject Classification

Primary 53-xx. Secondary 35P15, 53C40, 58C40.

Full Text (PDF format)

Received 28 November 2022

Received revised 15 June 2023

Accepted 20 October 2023

Published 1 June 2024