nLab
geometric measure theory

Contents

Idea

Geometric measure theory and geometric integration 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.

References