Oleksandr Metelichenko (University College London &
Odessa University)
Isodiametric problem in the groups with dilations
Abstract.
We show that the isodiametric inequality (a metric ball
maximizes the volume
for the given diameter) fails in the Heisenberg group
equipped with the
Carnot-Carath\'eodory (geodesic) metric and give estimates
for the ratio
of the volume of the ball and the maximal volume of a set
of the same diameter.
We also give some examples of the similar nature in the
additive group $\R^n$
with non-isotropic dilations.
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