Hypoellipticity: Geometrization and Speculation

To any finite collection of smooth real vector fields $X_j$ in $\reals^n$ we associate a metric in the phase space $T^*\reals^n$. The relation between the asymptotic behavior of this metric and hypoellipticity of $\sum X_j^2$, in the smooth, real analytic, and Gevrey categories, is explored

Global C^\nf Irregularity of the ∂ˉ\bar\partial--Neumann Problem for Worm Domains

No abstract available

Near equality in the Riesz-Sobolev inequality in higher dimensions

The Riesz-Sobolev inequality provides an upper bound for a trilinear expression involving convolution of indicator functions of sets. It is known that equality holds only for homothetic ordered triples of appropriately situated ellipsoids. We characterize ordered triples of subsets of Euclidean space $R^d$ that nearly realize equality, for arbitrary dimensions $d$, extending a result already known for $d=1$