User:Luca.Spolaor/sandbox

2020 Mathematics Subject Classification: Primary: 49Q15 [MSN][ZBL]

Rectifiable varifolds are a generalization of rectifiable sets in the sense that they allow for a density function to be defined on the set. They are also strictly connected to rectifiable currents, in fact to such a current one can always associate a varifold by putting aside the orientation.

Definitions

Definition 1 Let $m\leq n$. A m-Rectifiable varifold is a couple $(M, \theta)$, where $M$ is a m-dimensional Rectifiable set in $\mathbb R^n$ and $\theta$ is a $\mathcal H^m$ measurable function defined on $M$, called the density function. A varifold is calle integral rectifiable if $\theta$ is integer valued.

References

[Sim]	Leon Simon, "Lectures on Geometric Measure Theory". Proceedings of the centre for Mathematical Analysis. Australian National University, Canberra, 1983. MR0756417Zbl 0546.49019
[FX]	Lin Fanghua, Yang Xiaoping, "Geometric Measure Theory-An Introduction". Advanced Mathematics Vol.1. International Press, Boston, 2002. MR2030862Zbl 1074.49011