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September 23, 2025Open Access

Backwards uniqueness for Mean curvature flow with asymptotically conical singularities

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Authors

JDJ. M. Daniels-HolgateHebrew University of JerusalemOHOr HershkovitsHebrew University of Jerusalem

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Implication

This analysis reveals backwards uniqueness in mean curvature flows at singularities, showing their relation.

Key Points

  • Backwards uniqueness is demonstrated for mean curvature flows encountering isolated asymptotically conical singularities.
  • Finding that if two hypersurfaces meet at the singular time, they will be the same before that time is significant.
  • New global tools were developed to address both the singularity's core and the flows' smooth parts together.
  • This research marks a notable advancement in understanding geometric flows with singularities.

Cite This Study

Daniels-Holgate et al. (2025) studied this question.

synapsesocial.com/papers/68d4759931b076d99fa6db60https://doi.org/10.48550/arxiv.2507.16805
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1On the structure of singularities of weak mean curvature flows with mean curvature bounds2025
  2. 2On the structure of singularities of weak mean curvature flows with mean curvature bounds2025
  3. 3How close is too close for singular mean curvature flows?2026
  4. 4Closed mean curvature flows with asymptotically conical singularities2024 · 1 citations
  5. 5Blow Up of Compact Mean Curvature Flow Solutions with Bounded Mean Curvature2024