Geodesic
Kähler–Einstein metrics with edge singularities
Thalia Jeffres1 ; Rafe Mazzeo2 ; Yanir A. Rubinstein3
1 Wichita State University, Wichita, KS
2 Stanford University, Stanford, CA
3 University of Maryland, College Park, MD
Annals of mathematics, Tome 183 (2016) no. 1, pp. 95-176.

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This article considers the existence and regularity of Kähler–Einstein metrics on a compact Kähler manifold $M$ with edge singularities with cone angle $2\pi \beta$ along a smooth divisor $D$. We prove existence of such metrics with negative, zero and some positive cases for all cone angles $2\pi \beta \leq 2\pi$. The results in the positive case parallel those in the smooth case. We also establish that solutions of this problem are polyhomogeneous, i.e., have a complete asymptotic expansion with smooth coefficients along $D$ for all $2\pi \beta < 2\pi$.
DOI : 10.4007/annals.2016.183.1.3

Thalia Jeffres 1 ; Rafe Mazzeo 2 ; Yanir A. Rubinstein 3

1 Wichita State University, Wichita, KS
2 Stanford University, Stanford, CA
3 University of Maryland, College Park, MD 
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Thalia Jeffres; Rafe Mazzeo; Yanir A. Rubinstein. Kähler–Einstein metrics with edge singularities. Annals of mathematics, Tome 183 (2016) no. 1, pp. 95-176. doi : 10.4007/annals.2016.183.1.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2016.183.1.3/

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