Geometric measure theory studies various measures of subsets of Euclidean spaces (and possibly of some geometric generalizations) and their geometric properties. Especially, one studies rectifiability of subsets of some lower dimensionality, to define notions like area, arc length etc. and to study distributions and currents on such spaces. Very central questions and motivations belong to the variational problems including the study of minimal surfaces.
H. Federer, W. H. Fleming, Normal and integral currents, Ann. of Math. (2) 72 1960 458–520, MR123260, doi
Stephen H. Schanuel, What is the length of a potato? An introduction to geometric measure theory, in: Categories in continuum physics (Buffalo, N.Y., 1982), 118–126, Lecture Notes in Math. 1174, Springer 1986, MR842922,doi
Revised on May 25, 2012 16:15:44
by Zoran Škoda