Critical Points of the Weighted Area Functional

Abstract

In this survey, we discuss critical points of functionals by various aspects. We review properties of critical points of weighted area functional, that is, self-shrinkers of mean curvature flow in Euclidean spaces and examples of compact self-shrinkers are discussed. We also review properties of critical points for weighted area functional for weighted volume-preserving variations, that is, \(\lambda \)-hypersurfaces of weighted volume-preserving mean curvature flow in Euclidean spaces.