Work

How close is too close for singular mean curvature flows?

Year: 2026

Type: article

Abstract: Suppose $$(M^i_t)_{t\in [0,T)}$$ ( M t i ) t ∈ [ 0 , T ) , $$i=1,2$$ i = 1 , 2 , are two mean curvature flows in $$\mathbb {R}^{n+1}$$ R n + 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, $$d_H$$ d H , satisfies $$d_{H}(M^1_t,M^2_t)/(T-t)^k \rightarrow 0$$ d H ( M t 1 , M t 2 ) / ( T - t ) k → 0 . We demonstrate that $$M^1_t=M^2_t$$ M t 1 = M t 2 for every t . This generalizes a result of Martin-Hagemayer and Sesum, who proved the case where $$M^1_t$$ M t 1 is itself a self-similarly shrinking flow.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-026-03403-4

Authors: J. M. Daniels-Holgate, Or Hershkovits

Institutions: Queen Mary University of London, Hebrew University of Jerusalem

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Engineering and Physical Sciences Research Council, HORIZON EUROPE European Research Council