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Institute of Stochastics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.056 und 2.002

Address
Hausadresse:
Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Englerstr. 2
D-76131 Karlsruhe

Postadresse:
Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Postfach 6980
D-76049 Karlsruhe

Office hours:
Mo-Fr 10:00 - 12:00

Tel.: +49 721 608 43270/43265

Fax.: +49 721 608 46066

Publications

Preprints

  • Regularly varying functions, generalized contents, and the spectrum of fractal strings, Preprint 2017, 29 pages (with Tobias Eichinger) arXiv:1703.09140
  • Localization results for Minkowski contents, Preprint 2016, 29 pages arXiv:1610.03117

Published articles

  • 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)