A local Steiner–type formula for general closed sets and applications

By Daniel Hug, Günter Last, Wolfgang H. Weil. 2004

127 citations recorded by the source corpus.

Subfields: Applied Mathematics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/6b16107a90737099972ac3dd6f4deaa5d833f276

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Signal Processing

Citations in the corpus

Outer Minkowski content for some classes of closed sets (2008, background): “In connection with the most recent developments on this subject we mention the paper [12], where the authors present a generalization of the Steiner formula to closed sets; nevertheless such general formula is not polynomial in r, and so the existence of the outer Minkowski content cannot be obtaine”
Curvature measures and fractals (2008, methodology): “Except for the support measures of Hug, Last and Weil [14], most fractal sets are not included in any of the set classes for which curvature measures can be defined.”
Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators (2010, background): “1; see [8,37,13] and [40, 2,12], in particular.”
COMPUTATION OF THE PERIMETER OF MEASURABLE SETS VIA THEIR COVARIOGRAM. APPLICATIONS TO RANDOM SETS (2011, background): “This measure has different names, depending on its normalization and the degree of generalization: intrinsic volume of index d− 1 and Minkowski’s content of index 1 for convex sets [24], total curvature of index d − 1 for sets with positive reach and UPR-sets [9, 22], or also in a more general setti”
On volume and surface area of parallel sets (2009, methodology): “(Note that the counterexamples of Ferry [5] mentioned in [9] do not disclaim rectifiability.”
Moments and Central Limit Theorems for Some Multivariate Poisson Functionals (2012, background): “α A,d(x,u) , where N(A) is the unit normal bundle of A. This consists of all pairs (x,u) ∈ Rd × Sd−1 that occur as unique nearest point and associated direction of a point in the complement of A, see [6]. The homogeneity (6.5) follows from the homogeneity of the (non-negative) measure 1{(x,u) ∈ N(A)”