How close is too close for singular mean curvature flows?

2025/03/14 by Daniels-Holgate, Joshua, Hershkovits, Or · 3 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.11522

Abstract

Suppose (Mⁱ_t)_{t∈ [0,T)}, i=1,2, are two mean curvature flows in ℝⁿ⁺¹ encountering a multiplicity one compact singularity at time T, in such a manner that for every k, the Hausdorff distance between the two flows, d_H, satisfies d_H(M¹_t,M²_t)/(T-t)^k → 0. We demonstrate that M¹_t=M²_t for every t. This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where M¹_t is itself a self-similarly shrinking flow.

Cited by

• Decay order bound for mean curvature flow near compact singularities
• On the rate of convergence of cylindrical singularity in mean curvature flow
• Backwards uniqueness for Mean curvature flow with asymptotically conical singularities

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