In this article, we prove a sharp isoperimetric inequality in the generalized Grushin plane depending on a parameter $\alpha>0$. For each $\alpha$ we compute the corresponding isoperimetric sets. We also discuss the connection of the problem with the Heisenberg isoperimetric problem.
Isoperimetric inequality in the Grushin plane
MONTI, ROBERTO;
2004
Abstract
In this article, we prove a sharp isoperimetric inequality in the generalized Grushin plane depending on a parameter $\alpha>0$. For each $\alpha$ we compute the corresponding isoperimetric sets. We also discuss the connection of the problem with the Heisenberg isoperimetric problem.
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