Geodesic
An Onofri-type Inequality on the Sphere with Two Conical Singularities
Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 663-672

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DOI

In this paper, we give a new proof of the Onofri-type inequality $$\int_{S}{{{e}^{2u}}\,d{{s}^{2}}\,\le \,4\pi (\beta \,+\,1)\,\text{exp}}\left\{ \frac{1}{4\pi (\beta \,+\,1)}{{\int_{S}{\left| \nabla u \right|}}^{2}}\,d{{s}^{2}}\,+\,\frac{1}{2\pi (\beta \,+\,1)}\,\int_{S}{u\,d{{s}^{2}}} \right\}$$ 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.
DOI : 10.4153/CMB-2011-115-4
Mots-clés : 53C21, 35J61, 53A30 
Zhou, Chunqin. An Onofri-type Inequality on the Sphere with Two Conical Singularities. Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 663-672. doi: 10.4153/CMB-2011-115-4
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     author = {Zhou, Chunqin},
     title = {An {Onofri-type} {Inequality} on the {Sphere} with {Two} {Conical} {Singularities}},
     journal = {Canadian mathematical bulletin},
     pages = {663--672},
     year = {2012},
     volume = {55},
     number = {3},
     doi = {10.4153/CMB-2011-115-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-115-4/}
}
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