Calculus of Variations and Geometric Measure Theory

V. Kivioja - E. Le Donne - S. Nicolussi Golo

Metric equivalences of Heintze groups and applications to classifications in low dimension

created by ledonne on 07 Nov 2021



Inserted: 7 nov 2021
Last Updated: 7 nov 2021

Year: 2021

ArXiv: 2104.00368 PDF


We approach the quasi-isometric classification questions on Lie groups by considering low dimensional cases and isometries alongside quasi-isometries. First, we present some new results related to quasi-isometries between Heintze groups. Then we will see how these results together with the existing tools related to isometries can be applied to groups of dimension 4 and 5 in particular. Thus we take steps towards determining all the equivalence classes of groups up to isometry and quasi-isometry. We completely solve the classification up to isometry for simply connected solvable groups in dimension 4, and for the subclass of groups of polynomial growth in dimension 5.

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