Titlebook: Curvature Measures of Singular Sets; Jan Rataj,Martina Zähle Book 2019 Springer Nature Switzerland AG 2019 Curvature Measure.Gauss-Bonnet

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Book 2019 with positive reach and some extensions, which include the classical polyconvex sets and piecewise smooth submanifolds as special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable curren

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Canon Questions: Art in ‘Black Britain’ and results from this chapter can be found in the Federer’s book [.] and/or in the book of Krantz and Parks [.]. Other sources will be cited when needed. Most of these results are presented without proofs.

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B. A. E. Meekings,T. P. Kudrycki,M. D. Sorensions: the polyconvex sets and the piecewise smooth submanifolds, respectively. Therefore the natural question arises whether we can consider unions of sets with positive reach under the above aspects.

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https://doi.org/10.1007/978-1-349-12804-4tions. A classical and comprehensive reference to integral-geometric relations is the book of Santaló [.]. In this chapter we derive integral-geometric formulas concerning curvature measures and their total values (total curvatures or intrinsic volumes). This is, in particular, the Principal kinemat

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https://doi.org/10.1007/978-1-349-00216-0y .). This stability result motivates a natural question whether curvature measures of more general sets can be introduced through approximation with parallel sets. This will indeed be the case, as it will be clear in Chap. .. However, not only parallel sets may be used for approximation. Classicall

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https://doi.org/10.1057/978-1-137-54060-7ive reach). This setting is still not satisfactory since it does not encompass some natural set classes as closures of complements to convex bodies, or boundaries of convex bodies, though these sets should apparently admit a natural definition of curvatures.

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Curvature Measures of Singular Sets978-3-030-18183-3Series ISSN 1439-7382 Series E-ISSN 2196-9922