A rigidity theorem of ancient solutions to the mean curvature flow in codimension one
Qun Chen, Hongbing Qiu
TL;DR
This paper proves a rigidity theorem for complete noncompact ancient solutions to the mean curvature flow in codimension one, using point-wise estimates and establishing an optimal growth condition.
Contribution
It introduces a new rigidity theorem for ancient solutions in mean curvature flow and derives an optimal growth condition.
Findings
Rigidity theorem for ancient solutions
Point-wise estimate for second fundamental form
Optimal growth condition established
Abstract
By carrying out a point-wise estimate for the second fundamental form, we prove a rigidity theorem of complete noncompact ancient solutions to the mean curvature flow in codimension one. Moreover, we derive an optimal growth condition.
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Taxonomy
TopicsMathematics and Applications · Algebraic and Geometric Analysis · History and Theory of Mathematics