Robert Hardt


Rice University


Tuesday, March 12, 2019 - 4:00pm



RH 306

A k dimensional varifold on R^n is a Radon measure on the Grassmann bundle R^n x G(n,k) of k planes in R^n. Varifolds were originally introduced to describe limiting behavior of minimizing sequences of functions, paths, or surfaces. Stationary one-dimensional rectifiable varifolds have a simple regularity description due to F.Almgren and W.Allard (1976).  Oriented 1d varifolds are useful in describing various optimal transport problems. Also, signed 1d varifolds can be used to model Michell trusses. These are cost minimal 1d balanced structures consisting of beams and cables. Introduced in 1904, they have been treated in the Mechanical Engineering  literature and in interesting mathematics 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. The varifold model allows one to consider associated evolution and higher dimensional problems.