Extension of Two-Dimensional Mean Curvature Flow with Free Boundary

  • Siao-Hao GuoEmail author


Given a mean curvature flow of compact, embedded \(C^{2}\) surfaces satisfying Neumann free boundary condition on a mean convex, smooth support surface in 3-dimensional Euclidean space, we show that it can be extended as long as its mean curvature and perimeter stay uniformly bounded along the flow.


Mean curvature flow Free boundary Extension problem 



The author is grateful to Peter Sternberg for suggesting the problem, for insightful discussions and for providing helpful comments on this paper.


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Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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