High Quality Content by WIKIPEDIA articles! In mathematics, a varifold is, loosely speaking, a measure-theoretic generalization of the concept of a differentiable manifold, by replacing differentiability requirements with those provided by rectifiable sets, while maintaining the general algebraic structure usually seen in differential geometry. More closely, varifolds generalize the ideas of a rectifiable current. Varifolds are the topic of study in geometric measure theory. Given an open subset ? of Euclidean space scriptstylemathbb{R}^n, an m-dimensional varifold on ? is defined as a Radon measure on the set Omega times G(n,m) where G(n,m) is the Grassmannian of all m-dimensional linear subspaces of an n-dimensional vector space.

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