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On the existence and uniqueness of ancient rescaled mean curvature flows
Open accessAbstract
We show existence of ancient solutions to the rescaled mean curvature flow starting from a given asymptotically conical self-expander. These are examples of mean curvature flows coming out of cones that are not self-similar. We also show a strong uniqueness theorem when the cone is generic and use it to classify mean curvature flows coming out of generic cones of small entropy in low dimensions.
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References 3 · Cited by 4
Metadata
- Authors
- Chen, L.
- Affiliations
- Zhejiang Normal University (CN)
- Corresponding author
- Chen, Letian
- ORCID
- Chen, Letian
- Venue
- Communications in Analysis and Geometry
- Publisher
- International Press of Boston
- Published
- 2026
- Pages
- 1-45
- ISSN
- 1019-8385 (ISSN-L)
- 1944-9992
- OpenAlex
- W4312107639
- Cited by
- 4
- References
- 3
- Citations by year
- 2026: 3
- FWCI
- 6.59
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Communications in Analysis and Geometry (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Geometry Research
- Physical Sciences › Mathematics › Applied Mathematics › Nonlinear Partial Differential Equations
- Keywords
- mean curvature flow, ancient solutions, uniqueness theorem, entropy, singularity formation
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- CoChat. (2026). Citation check: On the existence and uniqueness of ancient rescaled mean curvature flows. https://app.cochat.ai/papers/10.4310/cag.260928092010
- The paper
- Chen, L. (2026). On the existence and uniqueness of ancient rescaled mean curvature flows. Communications in Analysis and Geometry. https://doi.org/10.4310/cag.260928092010
