Comparison theorems for exit times

By Almut Burchard, Michael Schmuckenschläger. 2001

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Compactness via symmetrization (2004, background): “We are not aware of estimates for the difference between the two sides of Riesz’ rearrangement inequality in the literature, even though such estimates are readily obtained for the simpler twopoint rearrangement [25, 26].”
Rearrangement inequalities for functionals with monotone integrands (2005, background): “Equality cases have also been determined in these situations [27, 5, 25, 26].”
Robust Optimality of Gaussian Noise Stability (2012, background): “First, Isaksson and the first author [20] applied some recent advances in spherical symmetrization [10] to give an proof that also generalizes to a problem involving more than two Gaussian vectors.”