Curvature measures and fractals
Steffen Winter
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Curvature measures are an important tool in geometric measure theory and other fields of mathematics for describing the geometry of sets in Euclidean space. But the ’classical’ concepts of curvature are not directly applicable to fractal sets. We try to bridge this gap between geometric measure theory and fractal geometry by introducing a notion of curvature for fractals. For compact sets (e.g. fractals), for which classical geometric characteristics such as curvatures or Euler characteristic...