Publications by Steffen Winter

Preprints

• Anna Rozanova-Pierrat, Alexander Teplyaev, Steffen Winter, Martina Zähle: Fractal curvatures and short-time asymptotics of heat content, Preprint 2025 arXiv:2502.02989

Published articles

• Jan Rataj, Steffen Winter: On volume and surface area of parallel sets. II. Surface measures and (non)differentiability of the volume, Bull. London Math. Soc. (2025) doi:10.1112/blms.70006 (Preprint: arXiv:2301.07429)

• Tillmann Bosch, Steffen Winter: On the radial growth of ballistic aggregation and other aggregation models, J. Stat. Phys. 191:42 (2024) doi:10.1007/s10955-024-03256-1 (Preprint: arXiv:2308.13193)

• Michael A. Klatt, Steffen Winter: Almost sure convergence and second moments of geometric functionals of fractal percolation, Adv. Appl. Probab. 56, 927–959 (2024) doi.org/10.1017/apr.2023.48 (Preprint: arXiv:2204.05878)

• Jan Rataj, Steffen Winter, Martina Zähle: Mean Lipschitz-Killing curvatures for homogeneous random fractals, J. Fractal Geom. 10 (2023), no. 1, 1–42 doi:10.4171/jfg/124 (Preprint: arXiv:2107.14431)

• Felix Ernesti, Matti Schneider, Steffen Winter, Daniel Hug, Günter Last, Thomas Böhlke: Characterizing digital microstructures by the Minkowski-based quadratic normal tensor, Math. Meth. Appl. Sci. 46 (2023), no.1, 961-985, doi.org/10.1002/mma.8560 (Preprint: arXiv:2007.15490)

• Tim Gutjahr, Sina Hale, Karsten Keller, Philipp Blum, Steffen Winter: Quantification of fracture roughness by change probabilities and Hurst exponents, Math. Geosc. 54 (2022), 679-710 doi:10.1007/s11004-021-09985-3 (Preprint: arXiv:2111.08661)

• Michael A. Klatt, Steffen Winter: Geometric functionals of fractal percolation, Adv. Appl. Prob. 52 (2020), no. 4, 1085-1126 doi:10.1017/apr.2020.33 (Preprint: arXiv:1812.06305)

• Steffen Winter: Localization results for Minkowski contents, J. Lond. Math. Soc. 99 (2019), no.2, 553-582 doi:10.1112/jlms.12180 (Preprint: arXiv:1610.03117)

• Tobias Eichinger, Steffen Winter: 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 (Preprint: arXiv:1703.09140)

• Sabrina Kombrink, Steffen Winter: Lattice self-similar sets on the real line are not Minkowski measurable, Ergodic Theory and Dynamical Systems (2018), 1-12 doi:10.1017/etds.2018.26 (Preprint: arXiv:1801.08595)

• Sabrina Kombrink, Erin Pearse, Steffen Winter: Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable, Math. Z. 283 (2016), 1049-1070 doi:10.1007/s00209-016-1633-x (Preprint: arXiv:1501.03764)

• Steffen Winter: Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets, Adv. Math. 274 (2015), 285-322 doi:10.1016/j.aim.2015.01.005 (Preprint: arXiv:1403.5201)

• Evgeny Spodarev, Peter Straka, Steffen Winter: Estimation of fractal dimension and fractal curvatures from digital images, Chaos, Solitons & Fractals 75 (2015), 134–152 doi:j.chaos.2015.02.011 (Preprint: arXiv:1408.6333)

• Dusan Pokorny, Steffen Winter: Scaling exponents of curvature measures, J. Fractal Geom. 1 (2014), 177–219 doi:10.4171/JFG/5 (Preprint: arXiv:1307.5053)

• Jan Rataj, Steffen Winter: Characterization of Minkowski measurability in terms of surface area, J. Math. Anal. Appl. 400 (2013), 120-132 doi: 10.1016/j.jmaa.2012.10.059 arXiv:1111.1825

• Michel L. Lapidus, Erin Pearse, Steffen Winter: 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 arxiv:1104.1641

• Steffen Winter, Martina Zähle: Fractal curvature measures of self-similar sets, Adv. Geom. 13 (2013), no. 2, 229–244 doi: 10.1515/advgeom-2012-0026 arxiv:1007.0696

• Erin Pearse, Steffen Winter: Geometry of canonical self-similar tilings, Rocky Mountain J. Math. 42 (2012), no. 4, 1327–1357 arxiv:0811.2187

• Steffen Winter: Curvature bounds for neighborhoods of self-similar sets, Comment. Math. Univ. Carolin. 52 (2011), no. 2, 205-226 arxiv:1010.2032

• Michel L. Lapidus, Erin Pearse, Steffen Winter: Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators, Adv. Math. 227 (2011), 1349–1398 doi:10.1016/j.aim.2011.03.004

• Steffen Winter: Lower S-dimension of fractal sets, J. Math. Anal. Appl. 375 (2011), no. 2, 467-477 dx.doi.org/10.1016/j.jmaa.2010.09.047

• Jan Rataj, Steffen Winter: On volume and surface area of parallel sets, Indiana Univ. Math. J. 59 (2010), no. 5, 1661–1685 jstor:24903398

• Steffen Winter: Geometric measures for fractals, in: J. Barral, S. Seuret, Recent developments in fractals and related fields, Birkhäuser, 2010, pp 73-89 pdf

• Marianna Csörnyei, Bernd Kirchheim, Toby C. O'Neil, David Preiss, Steffen Winter: Universal singular sets in the calculus of variations, Arch. Ration. Mech. Anal. 190 (2008), no. 3, 371-424 doi:10.1007/s00205-008-0142-4 (Preprint: arXiv:math/0609216)

• Steffen Winter: Curvature measures and fractals, Diss. Math. 453 (2008), 1-66

• Marta Llorente, Steffen Winter: A notion of Euler characteristic for fractals, Math. Nachr. 280 (2007), no. 1-2, 152-170

• Lars Olsen, Steffen Winter: 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

• Karsten Keller, Steffen Winter: Combinatorics of distance doubling maps, Fundam. Math. 187, No.1 (2005), 1-35

• Lars Olsen, Steffen Winter: 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

Edited volumes

• Uta Freiberg, Ben Hambly, Michael Hinz, Steffen Winter (editors): Fractal Geometry and Stochastics VI, Progress in Probability 76, Birkhäuser, Basel, 2021 doi:10.1007/978-3-030-59649-1 (Preprint 2020)

PhD thesis

• Curvature measures and fractals, Jena (2006) pdf

Diploma thesis

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