The growth of the first non-Euclidean filling function of the quaternionic Heisenberg Group

2017/02/03 by Gruber, Moritz
#20F18 #20F65 #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1702.00954

Abstract

The filling volume functions of the n-th quaternionic Heisenberg group grow, up to dimension n, as fast as the ones of the Euclidean space. We identify the growth rate of the filling volume function in dimension n+1, which is strictly faster than the growth rate of the (n+1)-dimensional filling volume function of the Euclidean space.

Related

• Higher Divergence Functions for Heisenberg Groups
• On a theorem of Hegyvári and Hennecart
• Rational growth in the Heisenberg group
• Filling inequalities for nilpotent groups
• The quaternionic Monge-Ampère operator and plurisubharmonic functions on the Heisenberg group