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Minimal surfaces in pseudohermitian geometry

Jih-Hsin Cheng, Jenn-Fang Hwang, Andrea Malchiodi, Paul Yang (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation...

Minkowski valuations intertwining the special linear group

Christoph Haberl (2012)

Journal of the European Mathematical Society

All continuous Minkowski valuations which are compatible with the special linear group are completely classified. One consequence of these classifications is a new characterization of the projection body operator.

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