Varifolds are a notion of generalized surfaces arising in geometric measure theory.
The concept has been introduced by Almgren to carry out the study of minimal surfaces. Though mainly used in the context of so-called "rectifiable sets", they turn out to be well suited to the study of discrete shapes as well. While the structure of varifold is flexible enough to adapt to both regular and discrete objects, it allows to define variational notions of mean curvature and second fundamental form based on the divergence theorem.
We propose to give a gentle introduction to varifolds, through various examples of shapes and with a special focus on generalized curvature.