Abstract
We give a new proof of Aubin's improvement of the Sobolev inequality on Sn; under the vanishing of 1st-order moments of the area element and generalize it to higher-order moments case. By careful study of an extremal problem on Sn, we determine the constant explicitly in the 2nd-order moments case.
Original language | English (US) |
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Pages (from-to) | 10822-10857 |
Number of pages | 36 |
Journal | International Mathematics Research Notices |
Volume | 2022 |
Issue number | 14 |
DOIs | |
State | Published - Jul 1 2022 |
ASJC Scopus subject areas
- General Mathematics