How close is too close for singular mean curvature flows?
Abstract
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 8
- Pages
- 234–234
- Publication date
- 18 July 2026
- Language
- EN