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arXiv · 1305.2968

A note on the area and coarea formulas for general volume densities and some applications

Daniel Cibotaru·Jorge de Lira
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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 $mathbb{R}^n$. A discussion about the first variation of the anisotropic area is also included.

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Daniel Cibotaru, Jorge de Lira. 2014-05-05. A note on the area and coarea formulas for general volume densities and some applications. https://arxiv.org/abs/1305.2968

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