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讲座题目:One Dimensional Rectifiable Varifolds and Some Applications
报告人:Robert Hardt, Moody Professor of Mathematics, Rice University, USA
报告时间与地点:2014年6月10日上午9:00-10:00天津大学第六教学楼111室
摘要:Varifolds were originally introduced to describe various 2 dimensional minimal surfaces and soap film models. A varifold is stationary in a region U if the first variation of its mass is zero under deformations supported in U. A stationary one-dimensional varifold may model a spider-web (possibly of variable thickness) where the region U is the complement of the attaching points for the web. With a suitable lower density bound, a stationary one dimensional rectifiable varifold enjoys a regularity property due to F. Almgren and W. Allard (1976). Here we discuss an application of signed varifolds to Michel trusses, which are cost optimal 1 dimensional balanced structures consisting of bars and cables. Introduced in a 1904 paper of an economist A.G. Michel, they have been treated in the Mechanical Engineering literature and in interesting papers by R. Kohn and G. Strang (1983) and by G. Bouchitte, W. Gangbo, and P. Sepulcher (2008). There are many basic open questions about the location and structure of Michel trusses.
天津大学应用数学中心