Lussardi, Luca; Villa, Elena A general formula for the anisotropic outer Minkowski content of a set. (English) Zbl 1345.28007 Proc. R. Soc. Edinb., Sect. A, Math. 146, No. 2, 393-413 (2016). Summary: We generalize to the anisotropic case some classical and recent results on the \((n-1)\)-Minkowski content of rectifiable sets in \(\mathbb{R}^n\), and on the outer Minkowski content of subsets of \(\mathbb{R}^n\). In particular, a general formula for the anisotropic outer Minkowski content is provided; it applies to a wide class of sets that are stable under finite unions. Cited in 6 Documents MSC: 28A75 Length, area, volume, other geometric measure theory 49Q15 Geometric measure and integration theory, integral and normal currents in optimization 52A39 Mixed volumes and related topics in convex geometry Keywords:Minkowski content; outer Minkowski content; anisotropy; rectifiability PDFBibTeX XMLCite \textit{L. Lussardi} and \textit{E. Villa}, Proc. R. Soc. Edinb., Sect. A, Math. 146, No. 2, 393--413 (2016; Zbl 1345.28007) Full Text: DOI References: [1] DOI: 10.1090/S0002-9947-1959-0110078-1 [2] DOI: 10.1051/ps/2011160 · Zbl 1395.62069 [3] Adv. Calc. Var. 7 pp 241– (2014) [4] DOI: 10.1051/m2an/2009044 · Zbl 1185.94008 [5] J. Multivariate Analysis 125 pp 68– (2014) [6] DOI: 10.1080/02331888.2013.800264 · Zbl 1367.62173 [7] DOI: 10.1239/aap/1246886612 · Zbl 1173.62016 [8] DOI: 10.1007/s00208-008-0254-z · Zbl 1152.28005 [9] Functions of bounded variation and free discontinuity problems (2000) · Zbl 0957.49001 [10] DOI: 10.3150/12-BEJ474 · Zbl 1291.60025 [11] DOI: 10.5566/ias.v29.p111-119 · Zbl 1228.60024 [12] DOI: 10.1007/s10231-008-0093-2 · Zbl 1173.28002 [13] Lectures on geometric measure theory. 3 (1983) · Zbl 0546.49019 [14] DOI: 10.1046/j.1365-2818.2002.01041.x [15] DOI: 10.1007/s00440-005-0459-y · Zbl 1099.60011 [16] DOI: 10.1007/s00209-003-0597-9 · Zbl 1059.53061 [17] DOI: 10.1006/cviu.1998.0674 · Zbl 05469048 [18] Geometric measure theory (1969) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.