Variability sets on Riemann surfaces and forgetful maps between Teichmüller spaces.
Variation of quasiconformal mappings on lines
We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Hölder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.
Versions of Koebe 1/4 Theorem for Analytic and Quasiregular Harmonic Functions and Applications
Verzerrungsaussagen bei quasikonformen Abbildungen mit ortsabhängiger Dilationsbeschränkung und ein Extremalprinzip der Elektrostatik in inhomogenen Medien.