Riemann integration, Lebesgue integration
line integral/contour integration
integration of differential forms
integration over supermanifolds, Berezin integral, fermionic path integral
Kontsevich integral, Selberg integral, elliptic Selberg integral
integration in ordinary differential cohomology
integration in differential K-theory
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.
Herbert Federer, Geometric measure theory, Grundlehren 153, Springer (1969, 1996) [doi:10.1007/978-3-642-62010-2]
Victor Guillemin, Shlomo Sternberg, Geometric asymptotics, Mathematical Surveys and Monographs 14, AMS (1977) [ams:surv-14]
Jürgen Jost, The geometric calculus of variations: a short survey and a list of open problems, Exposition. Math. 6 (1988), no. 2, 111–143, MR89h:58036
Steven G. Krantz, Harold Parks, Geometric integration theory, Springer (2008) [pdf]
Frederick J., Jr. Almgren, Almgren’s big regularity paper (book form of a 1970s preprint)
F. J. Almgren, Jr., Geometric measure theory and elliptic variational problems, Proc. ICM Nice 1970, vol. 2, djvu:350 K, pdf:649 K
Frank Morgan, Geometric measure theory: a beginner’s guide, Academic Press (2016) [doi:10.1016/C2015-0-01918-9]
eom: T.C.O’Neil (2001), Geometric measure theory
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
Rodolfo Rios-Zertuche, The variational structure of the space of holonomic measures, arxiv1408.5785
See also:
Last revised on June 10, 2023 at 07:37:03. See the history of this page for a list of all contributions to it.