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Quantitative long range curvature estimate for mean curvature flow

  • Jingze Zhu ORCID logo EMAIL logo
Published/Copyright: September 25, 2025

Abstract

We prove that 𝛼-noncollapsed ancient mean curvature flow satisfies a quantitative curvature estimate H ⁢ ( y , t ) ≤ C ⁢ H ⁢ ( x , t ) ⁢ ( H ⁢ ( x , t ) ⁢ | x − y | + 1 ) 2 for any pair of x , y . In other words, the rescaled curvature grows at most quadratically in terms of the rescaled extrinsic distance.

Acknowledgements

The author would like to thank his advisor Simon Brendle for giving insightful ideas.

References

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Received: 2024-11-23
Revised: 2025-06-09
Published Online: 2025-09-25
Published in Print: 2025-11-01

Š 2025 Walter de Gruyter GmbH, Berlin/Boston

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