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We introduce support (curvature) measures of an arbitrary closed set A in ℝ d and establish
a local Steiner–type formula for the localized parallel volume of A. We derive some of the …

We consider maps of the family of convex bodies in Euclidean $ d $-dimensional space into
itself that are compatible with certain structures on this family: A Minkowski-endomorphism is …

The problem considered belowis that of determining information about the topology of a
subset X⊂ ℝ n given only a finite point approximation to X. The basic approach is to …

Extending the celebrated results of Alexandrov (1958) and Korevaar–Ros (1988) for smooth
sets, as well as the results of Schneider (1979) and the first author (1999) for arbitrary …

Gradient structures are inhomogeneous along a particular gradient direction but
homogeneous perpendicular to that direction. Consequently, structural parameters such as …

This work is devoted to the investigation of the basic interrelations between the geometry of
convex sets and certain measures (or functionals), curvatures and currents which are …

Stationary random closed sets Ξ in Rd are considered whose realizations belong to the
extended convex ring. A new approach is proposed to joint estimation of the specific intrinsic …

Let B (“black”) and W (“white”) be disjoint compact test sets in ℝd, and consider the volume
of all its simultaneous shifts kee** B inside and W outside a compact set A⊂ ℝd. If the …

A stationary Boolean model is the union set of random compact particles which are attached
to the points of a stationary Poisson point process. For a stationary Boolean model with …