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One may define a trilinear convolution form on the sphere involving twofunctions on the sphere and a monotonic function on the interval $[-1,1]$. Asymmetrization inequality of Baernstein and Taylor states that this form ismaximized when the two functions on the sphere are replaced with theirnondecreasing symmetric rearrangements. In the case of indicator functions, weshow that under natural hypotheses, the symmetric rearrangements are the onlymaximizers up to symmetry by establishing a sharpened inequality.

A Sharpened Rearrangement Inequality for Convolution on the Sphere