Asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces
Liang Cheng, Natasa Sesum
TL;DR
This paper investigates the long-term behavior of Type III mean curvature flow on noncompact hypersurfaces using a new monotonicity formula related to self-expanders.
Contribution
It introduces a novel monotonicity formula and applies it to analyze the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces.
Findings
Established a new monotonicity formula for mean curvature flow.
Analyzed the asymptotic behavior of Type III flows on noncompact hypersurfaces.
Provided insights into the geometric evolution of noncompact hypersurfaces.
Abstract
In this paper, we introduce a monotonicity formula for the mean curvature flow which is related to self-expanders. Then we use the monotonicity to study the asymptotic behavior of Type III mean curvature flow on noncompact hypersurfaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research