Frequency of harmonic functions in Carnot groups and for operators of Baouendi type

Nicola Garofalo
Purdue University

I will discuss a generalization of Almgren's frequency to solutions of a sub-Laplacian (harmonic functions) on a Carnot group of arbitrary step or for the solutions of a closely connected class of degenerate second order operators of Baouendi type. The results discussed provide some new insight into the deep link existing between the growth properties of the frequency, and the local and global structure of the relevant harmonic functions in these non-Riemannian settings.

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