. "Scaling exponents of curvature measures" . "1"^^ . . . "2"^^ . . . . "locally flat; self-similar set; scaling exponent; fractal curvature; S-dimension; Minkowski dimension; curvature-direction measure; curvature measure; Parallel set"@en . "RIV/00216208:11320/14:10286403!RIV15-MSM-11320___" . . "43853" . . "Fractal curvatures of a compact set F in Rd are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets of F as diametr tends to 0 and have been studied in the last years in particular for self-similar and self-conformal sets. In the present paper we study the nongeneric situation when the scaling exponents are not determined by the dimension of F . We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R2. We expect local flatness to be characteristic also in higher dimensions. The results enlighten the geometric meaning of the scaling exponents." . . "[7633472C0075]" . "Fractal curvatures of a compact set F in Rd are roughly defined as suitably rescaled limits of the total curvatures of its parallel sets of F as diametr tends to 0 and have been studied in the last years in particular for self-similar and self-conformal sets. In the present paper we study the nongeneric situation when the scaling exponents are not determined by the dimension of F . We demonstrate that the possibilities for nongeneric behaviour are rather limited and introduce the notion of local flatness, which allows a geometric characterization of nongenericity in R and R2. We expect local flatness to be characteristic also in higher dimensions. The results enlighten the geometric meaning of the scaling exponents."@en . "Winter, Steffen" . . . "I, P(GCP201/10/J039)" . . "11320" . . "Scaling exponents of curvature measures"@en . "Scaling exponents of curvature measures" . . "2" . "10.4171/JFG/5" . . "Scaling exponents of curvature measures"@en . "Pokorn\u00FD, Du\u0161an" . . "43"^^ . . . . "CH - \u0160v\u00FDcarsk\u00E1 konfederace" . . "2308-1309" . "2014/1" . "RIV/00216208:11320/14:10286403" . . . "Journal of fractal geometry" .