Hypoellipticity: Geometrization and Speculation

Abstract

To any finite collection of smooth real vector fields Xj in R we associate a metric in the phase space T ∗Rn. The relation between the asymptotic behavior of this metric and hypoellipticity of ∑ X j , in the smooth, real analytic, and Gevrey categories, is explored. To Professor P. Lelong, on the occasion of his 85th birthday. 

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