Using elementary convexity arguments involving the Legendre transformation and the Prekopa-Leindler inequality, we prove the sharp Moser-Trudinger-Onofri inequality on the two-dimensional sphere.
Ghigi, A. (2005). On the Moser-Onofri and Prekopa-Leindler inequalities. COLLECTANEA MATHEMATICA, 56(2), 143-156.
On the Moser-Onofri and Prekopa-Leindler inequalities
GHIGI, ALESSANDRO CALLISTO
2005
Abstract
Using elementary convexity arguments involving the Legendre transformation and the Prekopa-Leindler inequality, we prove the sharp Moser-Trudinger-Onofri inequality on the two-dimensional sphere.
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