Consider a smooth, pseudoconvex CR structure on some small open set of real dimension three. A fundamental sufficient condition for an associated Cauchy-Riemann operator ∂̄b to be C ∞ hypoelliptic, modulo its nullspace (this notion is defined below in §4) is that the CR structure should be of finite type, but this condition is far from necessary. While some sufficient conditions are known [2] (s...

Let {Zj} be a finite collection of vector fields, with smooth complex-valued coefficients, defined in an open subset U of Euclidean space. Let Z∗ j be the formal adjoint of Zj , with respect to the Hilbert space structure L2 associated to some measure with a smooth nonvanishing density. Consider the operator L = ∑ j Z ∗ jZj, which we shall refer to as a sum of squares. L is said to be hypoellip...

In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the obtain blow-up type results and global in t-boundedness of solutions equations p-sub-Laplacian stratified