3 citations · 4 across the 7 of their papers we have counts for
7 papers
The Genus-Decreasing Property of Mean Curvature Flow, I
Brian White
This paper proves that, in mean curvature flow of a compact surface in a complete -manifold with Ricci curvature bounded below, the genus of the regular set is a decreasing func…
Generating Shrinkers by Mean Curvature Flow
David Hoffman, Francisco Martin, Brian White
We prove existence for many examples of shrinkers by producing compact, smoothly embedded surfaces that, under mean curvature flow, develop singularities at which the shrinkers occ…
Classification of Semigraphical Translators
Francisco Martín, Mariel Sáez, Raphael Tsiamis +1
We complete the classification of semigraphical translators for mean curvature flow in that was initiated by Hoffman-Martín-White. Specifically, we show that there i…
On the fundamental regularity theorem for mass-minimizing flat chains
Brian White
In the theory of flat chains with coefficients in a normed abelian group, we give a simple necessary and sufficient condition on a group element in order for the following fund…
Fattening in mean curvature flow
Tom Ilmanen, Brian White
For each , we prove existence of a compact, connected, smoothly embedded, genus- surface with the following property: under mean curvature flow, there is exactly o…
The Avoidance Principle for Noncompact Hypersurfaces Moving by Mean Curvature Flow
Brian White
Consider a pair of smooth, possibly noncompact, properly immersed hypersurfaces moving by mean curvature flow, or, more generally, a pair of weak set flows. We prove that if the am…
Helicoidal minimal surfaces of prescribed genus, I
David Hoffman, Martin Traizet, Brian White
For every genus g, we prove that S^2 x R contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also…