20,243 research outputs found

    Hypoellipticity: Geometrization and Speculation

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    To any finite collection of smooth real vector fields XjX_j in Rn\reals^n we associate a metric in the phase space Tβˆ—RnT^*\reals^n. The relation between the asymptotic behavior of this metric and hypoellipticity of βˆ‘Xj2\sum X_j^2, in the smooth, real analytic, and Gevrey categories, is explored

    Near equality in the Riesz-Sobolev inequality in higher dimensions

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    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 RdR^d that nearly realize equality, for arbitrary dimensions dd, extending a result already known for d=1d=1
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