A note on the area and coarea formulas for general volume densities and some applications
classification
🧮 math.DG
keywords
anisotropicareaapplicationscoareadensitiesformulasgeneralvolume
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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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