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1. CMB 2011 (vol 55 pp. 663)
An Onofri-type Inequality on the Sphere with Two Conical Singularities In this paper, we give a new proof of the Onofri-type inequality
\begin{equation*}
\int_S e^{2u} \,ds^2 \leq 4\pi(\beta+1) \exp \biggl\{
\frac{1}{4\pi(\beta+1)} \int_S |\nabla u|^2 \,ds^2 +
\frac{1}{2\pi(\beta+1)} \int_S u \,ds^2 \biggr\}
\end{equation*}
on the sphere $S$ with Gaussian curvature $1$ and with conical
singularities divisor $\mathcal A = \beta\cdot p_1 + \beta \cdot p_2$ for
$\beta\in (-1,0)$; here $p_1$ and $p_2$ are antipodal.
Categories:53C21, 35J61, 53A30 |