arXiv subjects

Daniele Morbidelli

Publications and source records attributed to Daniele Morbidelli.

20 records · Page 2Linked to original sources

arXiv2009

Liouville theorem, conformally invariant cones and umbilical surfaces for Grushin-type metrics

We prove a classification theorem for conformal maps with respect to the control distance generated by a system of diagonal vector fields. It turns out that all such maps can be obtained as compositions of suitable dilations, inversions and isometries. We also classify all umbilical surfaces of the underlying metric.

math.DG↗

arXiv2008

Stability of isometric maps in the Heisenberg group

In this paper we prove some approximation results for biLipschitz maps in the Heisenberg group. Namely, we show that a biLipschitz map with biLipschitz constant close to one can be pointwise approximated, quantitatively on any fixed ball, by an isometry. This leds to an approximation in BMO norm for the map's Pansu derivative. We also prove that a global quasigeodesic can be approximated by a geodesic in any fixed segment.

math.MG↗