Minimal Surfaces and Mean Curvature Flow

布莱恩·怀特计划研究平均曲率流，特别是奇点形成和被称为“增肥”的非唯一性。他还计划研究极小曲面如何依赖于其边界的总曲率，研究极小超曲面中奇点的密度边界，并寻找类螺旋曲面的新例子。布莱恩·怀特计划研究被称为“平均曲率流”的运动表面的行为。在数学中，平均曲率流和类似流已经被证明是非常重要的：特别是与之密切相关的“里奇流”，因为它在最近解决长期存在的庞加莱猜想中发挥了核心作用，所以经常出现在新闻中。平均曲率流也在自然界中出现。例如，退火金属中的晶界通过平均曲率流动移动。怀特还将研究平均曲率流处于平衡状态的表面。在自然界中，肥皂膜就是这种平衡的例子。

Brian White plans to investigate mean-curvature flow, particularly singularity formationand the non-uniqueness known as "fattening''. He also plans to study how minimal surfaces depend on the total curvature of their boundaries, to investigate density bounds for singularities in minimal hypersurfaces, and to search for new examples of helicoid-like minimal surfaces.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.