Minimal Surfaces and Mean Curvature Flow

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Brian White planes to investigate curvature blow up in sequences of minimal surfaces. He also plans to study how curvature blows up in sequences of minimal surfaces, to study how minimal surfaces depend on the total curvature of their boundaries, to investigate density bounds for singularites in minimal hypersurfaces, and to search for new examples of helicoid-like minimal surfaces. He also plans to investigate mean-curvature flow, particularly singularity formation and the non-uniqueness known as "fattening''. Brian White plans to investigate the behavior of surfaces that move by the process called "mean curvature flow". In mathematics, mean curvature flow and similar flows have proved to be very important: in particular, the closely related "ricci flow" has been very much in the news because of its central role in the recent solution of the long-standing Poincare conjecture. Mean curvature flow also arises in nature. For example, grain boundaries in annealing metals move by the mean curvature flow. White will also investigate surfaces that are in equilibrium for the mean curvature flow. In nature, soap films are examples of such equilibria.