Dr Tapio Rajala, Academy of Finland Postdoctoral Researcher at University of Jyväskylä, is interested in geometric analysis and geometric measure theory in metric measure spaces. Here are some of the topics he has recently studied.
- Optimal mass transportation: Ricci-curvature bounds in metric spaces, existence of optimal maps.
- Lipschitz, Sobolev, BV-mappings: metric differentiation, area formulas, dimension distortion, extension domains.
- Local structure of sets and measures: densities, dimension, rectifiability, porosity.
- Fractal geometry: self-similar and self-affine sets, Moran type constructions.