Integration of differential forms on manifolds with locally finite variations. Part~II
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 34, Tome 333 (2006), pp. 66-85
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In the part I of the paper the $n$-dimensional $C^0$-manifolds in $\mathbb R^n$ $(m\ge n)$ with locally finite $n$-dimensional variations (a generalization of locally rectifiable curves to dimension $n>1$) and integration of measurable differential $n$-forms over such manifolds were defined. The main result of part II states that an $n$-dimensional manifold $C^1$-embedded in $\mathbb R^m$ has locally finite variations and the integral of measurable differential $n$-form defined in part I can be calculated by well-known formula.
@article{ZNSL_2006_333_a6,
author = {A. V. Potepun},
title = {Integration of differential forms on manifolds with locally finite variations. {Part~II}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {66--85},
publisher = {mathdoc},
volume = {333},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_333_a6/}
}
A. V. Potepun. Integration of differential forms on manifolds with locally finite variations. Part~II. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 34, Tome 333 (2006), pp. 66-85. http://geodesic.mathdoc.fr/item/ZNSL_2006_333_a6/