Inequalities for Eigenvalues of Polynomial Operator of Elliptic Operator in Divergence Form on Metric Measure Space

Abstract

In this paper, we prove some inequalities for eigenvalues of polynomial operator of elliptic operator in divergence form on a metric measure space isometrically immersed into an Euclidean space. As applications of the result, we also give some corresponding results on complete minimal submanifolds in Euclidean spaces and unit ball.