Improved Sobolev inequality under constraints


Abstract in English

We give a new proof of Aubins improvement of the Sobolev inequality on $mathbb{S}^{n}$ under the vanishing of first order moments of the area element and generalize it to higher order moments case. By careful study of an extremal problem on $mathbb{S}^{n}$, we determine the constant explicitly in the second order moments case.

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