A Sharp Inequality on the Exponentiation of Functions on the Sphere

Sun Yung Alice Chang, Changfeng Gui

Research output: Contribution to journalArticlepeer-review

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In this paper we show a new inequality that generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second inequality in the Szegö limit theorem on the Toeplitz determinants on the circle. On the other hand, this inequality is also a variant of several classical inequalities of Moser-Trudinger type on the sphere. The inequality incorporates the deviation of the center of mass from the origin into the optimal inequality of Aubin for functions with mass centered at the origin, and improves Onofri's inequality with the contribution of the shifting of the mass center explicitly expressed.

Original languageEnglish (US)
Pages (from-to)1303-1326
Number of pages24
JournalCommunications on Pure and Applied Mathematics
Issue number6
StatePublished - Jun 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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