Research interests
Fractal Geometry, Geometric Measure Theory, Stochastic Geometry, Dynamical Systems
Publications
- Normal and non-normal points of self-similar sets and divergence points of self-similar measures, J. Lond. Math. Soc., II. Ser. 67, No.1, 103-122 (2003); (with Lars Olsen)
- Multifractal analysis of divergence points of deformed measure theoretical Birkhoff averages. II: Non-linearity, divergence points and Banach space valued spectra, Bull. Sci. Math. 131, no. 6, 518--558 (2007).; (with Lars Olsen)
- Combinatorics of distance doubling maps, Fundam. Math. 187, No.1, 1-35 (2005); (with Karsten Keller)
- A notion of Euler characteristic for fractals, Math. Nachr. 280, no. 1-2, 152170 (2007); (with Marta Llorente)
- Curvature measures and fractals, Diss. Math. 453, 66pp (2008)
- Universal singular sets in the calculus of variations, Arch. Ration. Mech. Anal. 190, no. 3, 371-424 (2008); (with Marianna Csörnyei, Bernd Kirchheim, Toby C. O'Neil und David Preiss)
- Geometry of canonical self-similar tilings, Rocky Mountain J. Math. (to appear); (with Erin Pearse) arxiv.org/abs/0811.2187
- Geometric measures for fractals, in: J. Barral, S. Seuret: Recent developments in fractals and related fields, Birkhäuser (to appear) pdf
- On volume and surface area of parallel sets, Indiana Univ. Math. J. (to appear); (with Jan Rataj) pdf
- Sets of small lower S-dimension, Preprint 2010 arxiv.org/abs/1003.3776
- Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators, Preprint 2010 (with Michel Lapidus and Erin Pearse) arxiv.org/abs/1006.3807
PhD thesis
- Curvature measures and fractals, Jena (2006) pdf
Diploma thesis
- Convergence points and divergence points of self-similar measures, Greifswald (2001)