A Relation between Mean Curvature Flow Solitons and Minimal Submanifolds |
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Authors: | Knut Smoczyk |
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Affiliation: | Max-Planck-Institute for Mathematics in the Sciences (MIS), Inselstr. 22—26D-04103 Leipzig, Germany |
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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 where equals ℝ × N equipped with a warped product metric and show that a submanifold inN converges to a conformal soliton under the mean curvature flow in N if and only if its associatedsubmanifold in converges to a minimal submanifold under a rescaled mean curvature flow in . 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. |
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Keywords: | Solitons mean curvature flow |
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