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varifold
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, the varifold generalize the idea of a rectifiable current. Varifolds are one of the topics of study in geometric measure theory.
==Historical note==
Varifolds were first introduced by L.C. Young in , under the name "''generalized surfaces''".〔 In his commemorative papers describing the research of Almgren, writes that these are "''essentially the same class of surfaces''".〕〔See also the (2015 unpublished essay ) of Wendell Fleming.〕 Frederick Almgren slightly modified the definition in his mimeographed notes and coined the name ''varifold'': he wanted to emphasize that these objects are substitutes for ordinary manifolds in problems of the calculus of variations.〔 exactly writes:-"''I called the objects "varifolds" having in mind that they were a measure-theoretic substitute for manifolds created for the variational calculus''". As a matter of fact, the name is a portmanteau of ''variational'' ''manifold''.〕 The modern approach to the theory was based on Almgren's notes〔The first widely circulated exposition of Almgren's ideas is the book : however, the first systematic exposition of the theory is contained in the mimeographed notes , which had a far lower circulation, even if it is cited in Herbert Federer's classic text on geometric measure theory. See also the brief, clear survey by .〕 and laid down by William Allard, in the paper .
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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