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Abstract
Let $(M,g)$ be a compact K\"ahlerEinstein manifold with $c_1 > 0$. Denote by $K\to M$ the canonical linebundle, with total space $X$, and $X_0$ the singular space obtained by blowing down $X$ along its zero section. We employ a construction by Page and Pope and discuss an interesting multiparameter family of Poincar\'eEinstein metrics on $X$. One 1parameter subfamily $\{g_t\}_{t>0}$ has the property that as $t\searrow 0$, $g_t$ converges to a PE metric $g_0$ on $X_0$ with conic singularity, while $t^{1}g_t$ converges to a complete Ricciflat K\"ahler metric $\hat{g}_0$ on $X$. Another 1parameters subfamily has an edge singularity along the zero section of $X$, with cone angle depending on the parameter, but has constant conformal infinity. These illustrate some unexpected features of the Poincar\'eEinstein moduli space.
Original language  English 

Publication status  Published  10 Sep 2007 
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Projects
 1 Finished

Complete Einstein metrics of negative scalar curvature
Singer, M.
12/06/03 → 11/06/07
Project: Research