Minimal hypersurfaces in Rn as regular values of a function

Abstract

In this paper we prove that if M = /^_1(0) is a minimal hypersurface of Rⁿ, where / : V C Rⁿ -► R is a smooth function defined on a open set V, then / must satisfy the equation |V/|²A/ = |(V|V/|²,V/} for every x € M. We will also prove that if M is the zero level set of a homogeneous 2 polynomial, then M must be a Clifford minimal hypersurface.