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Improved Sobolev inequality under constraints

Published 20 Oct 2020 in math.CA and math.DG | (2010.10654v2)

Abstract: We give a new proof of Aubin's 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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Authors (2)

  1. Fengbo Hang 
  2. Xiaodong Wang 

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