A note on the area and coarea formulas for general volume densities and some applications
Differential Geometry
2014-05-06 v2
Abstract
We present the area and coarea formulas for Lipschitz maps, valid for general volume densities. As applications, we give a short, "euclidean" proof of the anisotropic Sobolev inequality and describe an anisotropic tube formula for hypersurfaces in . A discussion about the first variation of the anisotropic area is also included.
Keywords
Cite
@article{arxiv.1305.2968,
title = {A note on the area and coarea formulas for general volume densities and some applications},
author = {Daniel Cibotaru and Jorge de Lira},
journal= {arXiv preprint arXiv:1305.2968},
year = {2014}
}
Comments
24 pages