Minimal Surfaces and Mean Curvature Flow

布赖恩白色飞机调查曲率炸毁序列的最小曲面。他还计划研究曲率如何炸毁序列的最小曲面，研究如何最小曲面取决于总曲率的边界，调查密度界的奇点在最小超曲面，并寻找新的例子螺旋状极小曲面。他还计划研究平均曲率流，特别是奇点的形成和被称为“增肥”的非唯一性。 布赖恩白色计划调查的行为表面的移动过程称为“平均曲率流”。 在数学中，平均曲率流和类似的流被证明是非常重要的：特别是，密切相关的“里奇流”已经在新闻中非常多，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。 自然界中也有平均曲率流。 例如，退火金属中的晶界通过平均曲率流移动。 白色也将调查表面是在平衡的平均曲率流。在自然界中，肥皂膜就是这种平衡的例子。

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.