9 citations · 9 across the 4 of their papers we have counts for
6 papers
Generic mean curvature flow has finitely many singularities
J. M. Daniels-Holgate, Or Hershkovits, Gábor Székelyhidi
We show that for a generic compact initial surface in , and any generic compact initial mean convex hypersurface in higher dimensions, the mean curvature flow encount…
Non-uniqueness in Mean Curvature Flow: Non-canonical solutions via the parabolic Allen--Cahn
J. M. Daniels-Holgate
When mean curvature flow evolves non-uniquely, the flow is said to fatten. The work of Ilmanen shows that any weak MCF is supported inside the fattening, and work of Hershkovits--W…
Backwards uniqueness for Mean curvature flow with asymptotically conical singularities
J. M. Daniels-Holgate, Or Hershkovits
In this paper we demonstrate that if two mean curvature flows of compact hypersurfaces and encounter only isolated, multiplicity one, asymptotically conical singula…
How close is too close for singular mean curvature flows?
Joshua Daniels-Holgate, Or Hershkovits
Suppose , , are two mean curvature flows in encountering a multiplicity one compact singularity at time , in such a manner that f…
Mean Curvature Flow from Conical Singularities
Otis Chodosh, J. M. Daniels-Holgate, Felix Schulze
We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singulari…
Approximation of mean curvature flow with generic singularities by smooth flows with surgery
Joshua Daniels-Holgate
We construct smooth mean curvature flows with surgery that approximate weak mean curvature flows with only spherical and neck-pinch singularities. This is achieved by combining the…