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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.