A relation between mean curvature flow solitons and minimal submanifolds
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Submission date: 23. Jan. 1999
published in: Mathematische Nachrichten, 229 (2001), p. 175-186
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.