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We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension two surfaces, which is different from the conditions of Risa and Sinestrari in \cite{RS} and we also remove the condition that the second fundamental form is uniformly bounded when $t\in(-\infty, -1)$.
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참고문헌 (26)
참고문헌 신청
Ben Andrews / 2012 / Noncollapsing in mean-convex mean curvature flow / Geometry & Topology 16(3):1413~1418
B. Andrews / 2010 / Mean curvature ow of pinched submanifolds to spheres / J. Differential Geom 85(3):357~395
S. B. Angenent / 1989 / Nonlinear diffusion equations and their equilibrium states, 3 / Birkhauser :21~38
Sigurd Angenent / 2013 / Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow / Networks & Heterogeneous Media 8(1):1~8
S. Angenent / 2019 / Unique asymptotics of ancient convex mean curvature ow solutions / J. Differential Geom 111(3):381~455
B. Andrews / 2010 / Mean curvature ow of pinched submanifolds to spheres / J. Differential Geom 85(3):357~395
S. B. Angenent / 1989 / Nonlinear diffusion equations and their equilibrium states, 3 / Birkhauser :21~38
Sigurd Angenent / 2013 / Formal asymptotic expansions for symmetric ancient ovals in mean curvature flow / Networks & Heterogeneous Media 8(1):1~8
S. Angenent / 2019 / Unique asymptotics of ancient convex mean curvature ow solutions / J. Differential Geom 111(3):381~455
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