Near equality in the Riesz-Sobolev inequality in higher dimensions
Abstract
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 Rd that nearly realize equality, for arbitrary dimensions d, extending a result already known for d=1.
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