Joshua Daniels-Holgate- PhD
- PDRA at Queen Mary University of London
Joshua Daniels-Holgate
- PhD
- PDRA at Queen Mary University of London
About
3
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Introduction
Current institution
Publications
Publications (3)
![Left: A hypersurface M\documentclass[12pt]{minimal}...](publication/385661940/figure/fig1/AS:11431281290313778@1731553044650/Left-A-hypersurface-Mdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Left: The initial cone C\documentclass[12pt]{minimal}...](publication/385661940/figure/fig2/AS:11431281290257697@1731553044846/Left-The-initial-cone-Cdocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
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 singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface \d...
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 recent work of Choi-Haslhofer-Hershkovits, and Choi-Haslhofer-Hershkovits-White, establishing canonical neighbourhoods of such singularities, with suitable barriers to f...
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 recent work of Choi-Haslhofer-Hershkovits, and Choi-Haslhofer-Hershkovits-White, establishing canonical neighbourhoods of such singularities, with suitable barriers to f...
