Curvature measures and fractals

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Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators (2010, background): “) This paper is part of the program of the present authors to develop a fractal notion of curvature in terms of complex dimensions, and to relate it to other notions of curvature, especially as developed in [41,30].”
On volume and surface area of parallel sets (2009, methodology): “Remark: The upper S-dimension dimSA is closely related to the curvature scaling exponent sd−1(A) defined in [20].”