Jan Techter works on discrete geometric structures. The Discretization in Geometry and Dynamics project identifies his participation in research on discrete surfaces.[ref]
With Alexander I. Bobenko, Carl O. R. Lutz and Helmut Pottmann, he studied Laguerre geometry in spaces of different curvature and its application to incircular nets. The work treats contact between oriented spheres and planes as geometric data preserved by transformations.[ref]

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