Curvature measures and fractals

@inproceedings{Winter2008CurvatureMA,
  title={Curvature measures and fractals},
  author={Steffen Winter},
  year={2008}
}
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 F ⊆ R d (e.g. fractals), for which classical geometric characteristics such as curvatures or Euler… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 28 CITATIONS

References

Publications referenced by this paper.
SHOWING 1-10 OF 25 REFERENCES

Zähle, Curvatures and currents for unions of sets with positive reach II, Ann

Jan Rataj, Martina
  • Global Anal. Geom
  • 2001
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

On the Minkowski measurability of fractals

Kenneth J. Falconer
  • Proc. Am. Math. Soc
  • 1995
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Curvature measures and fractals

Steffen Winter
  • Ph.D. thesis,
  • 2006
VIEW 1 EXCERPT