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Polar Coordinates in Carnot groups II

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arxiv 2208.04913 v1 pith:JFAIWLWI submitted 2022-08-09 math.AP math.DGmath.MG

Jeremy T. Tyson This is my paper
classification math.APmath.DGmath.MG
keywords carnotpolarcoordinatesgroupgroupshorizontalpolarizablesystem
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abstract

A Carnot group is polarizable if it carries a homogeneous norm whose powers are fundamental solutions for the $p$-sub-Laplacian operators for all $1<p \le \infty$. Such groups also support a system of horizontal polar coordinates. We prove that the converse statement is true: if a Carnot group supports a horizontal polar coordinate system with suitable properties, then it is polarizable.

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