Webrelaunch 2020



  • Fractal Geometry and Stochastics VI (editors: Uta Freiberg, Ben Hambly, Michael Hinz, Steffen Winter), Preprint 2020
  • Characterizing digital microstructures by the Minkowski-based quadratic normal tensor, Preprint 2020, 33 pages (with Felix Ernesti, Matti Schneider, Daniel Hug, Günter Last and Thomas Böhlke) arXiv:2007.15490
  • Geometric functionals of fractal percolation, to appear in: Adv. Appl. Prob., 36 pages (with Michael A. Klatt) arXiv:1812.06305

Published articles

  • Regularly varying functions, generalized contents, and the spectrum of fractal strings, in Horizons of Fractal Geometry and Complex Dimensions, Contemporary Mathematics, vol. 731, Amer. Math. Soc., Providence, RI, 2019, pp. 63-94 doi:10.1090/conm/731/14673 (with Tobias Eichinger) arXiv:1703.09140

  • Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets, Adv. Math. 274 (2015), 285-322 doi:j.aim.2015.01.005 arXiv:1403.5201
  • Estimation of fractal dimension and fractal curvatures from digital images, Chaos, Solitons & Fractals 75 (2015), 134–152 (with Evgeny Spodarev and Peter Straka) arXiv:1408.6333
  • Minkowski measurability results for self-similar tilings and fractals with monophase generators, in: M. L. Lapidus, E. P. J. Pearse, M. van Frankenhuijsen (editors), Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics I: Fractals in Pure Mathematics, Contemp. Math. 600 (2013), 185-203 (with Michel L. Lapidus and Erin Pearse) arxiv:1104.1641
  • Geometry of canonical self-similar tilings, Rocky Mountain J. Math. 42 (2012), no. 4, 1327–1357 (with Erin Pearse) arxiv:0811.2187
  • Curvature bounds for neighborhoods of self-similar sets, Comment. Math. Univ. Carolin. 52 (2011), no. 2, 205-226 arxiv:1010.2032
  • Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators, Adv. Math. 227 (2011), 1349–1398 (with Michel L. Lapidus and Erin Pearse) doi:10.1016/j.aim.2011.03.004
  • On volume and surface area of parallel sets, Indiana Univ. Math. J. 59 (2010), no. 5, 1661–1685 (with Jan Rataj) pdf
  • Geometric measures for fractals, in: J. Barral, S. Seuret, Recent developments in fractals and related fields, Birkhäuser, 2010, pp 73-89 pdf
  • Universal singular sets in the calculus of variations, Arch. Ration. Mech. Anal. 190 (2008), no. 3, 371-424 (with Marianna Csörnyei, Bernd Kirchheim, Toby C. O'Neil and David Preiss)
  • Curvature measures and fractals, Diss. Math. 453 (2008), 1-66
  • A notion of Euler characteristic for fractals, Math. Nachr. 280 (2007), no. 1-2, 152-170 (with Marta Llorente)
  • Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. II: Non-linearity, divergence points and Banach space valued spectra, Bull. Sci. Math. 13(2007)1, no. 6, 518-558 (with Lars Olsen)

  • Combinatorics of distance doubling maps, Fundam. Math. 187, No.1 (2005), 1-35 (with Karsten Keller)
  • Normal and non-normal points of self-similar sets and divergence points of self-similar measures, J. Lond. Math. Soc., II. Ser. 67 (2003), no. 1, 103-122 (with Lars Olsen)

PhD thesis

  • Curvature measures and fractals, Jena (2006) pdf

Diploma thesis

  • Convergence points and divergence points of self-similar measures, Greifswald (2001)