English

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 mathbbRnmathbb{R}^n. 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}
}

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24 pages