Abstract:In this paper, we study the regular geometric behavior of the mean curvature flow (MCF) of submanifolds in the standard Gaussian metric space (R m+p , e −|x| 2 /m g) where (R m+p , g) is the standard Euclidean space and x ∈ R m+p denotes the position vector. Note that, as a special Riemannian manifold, (R m+p , e −|x| 2 /m g) has an unbounded curvature. Up to a family of diffeomorphisms on M m , the mean curvature flow we considered here turns out to be equivalent to a special variation of the "conformal mean … Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.