Minimal Surfaces and Mean Curvature Flow

最小曲面和平均曲率流

• 批准号: 1105330
• 负责人: Brian White
• 金额: $ 18.5万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1105330&HistoricalAwards=false
• 关键词: Minimal; Surfaces; Mean; Curvature; Flow

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.

Brian White Plans研究极小曲面序列中的曲率爆破。他还计划研究极小曲面序列中的曲率如何膨胀，极小曲面如何依赖于其边界的总曲率，极小超曲面中奇异点的密度界限，以及寻找螺旋面般的极小曲面的新例子。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。布莱恩·怀特计划研究通过“平均曲率流”过程移动的表面的行为。在数学中，平均曲率流和相似流已被证明是非常重要的：尤其是密切相关的“Ricci流”，因为它在最近解决长期存在的Poincare猜想中发挥了核心作用，所以一直在新闻中非常重要。自然界中也存在平均曲率流。例如，退火金属中的晶界随平均曲率流动而移动。怀特还将研究平均曲率流处于平衡状态的表面。在自然界，肥皂片就是这种平衡的例子。