We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
62/1998
A relation between mean curvature flow solitons and minimal submanifolds
Knut Smoczyk
Abstract
We derive a one to one correspondence between conformal solitons of the mean curvature flow in an ambient space N and minimal submanifolds in a different ambient space Ñ, where Ñ equals R x N equipped with a warped product metric and show that a submanifold in N converges to a conformal soliton under the mean curvature flow in N if and only if its associated submanifold in Ñ converges to a minimal submanifold under a rescaled mean curvature flow in Ñ. We then define a notion of stability for conformal solitons and obtain Lp estimates as well as pointwise estimates for the curvature of stable solitons.
