Formal theory of cornered asymptotically hyperbolic Einstein metrics (Q2318018)

In this paper, the author studies the formal existence and expansion of asymptotically Einstein metrics on manifold with corner. Using the recent work of \textit{M. Nozaki} et al. [J. High Energy Phys. 2012, No. 6, Paper No. 66, 25 p. (2012; Zbl 1397.81318)] the author generalizes and extends the theory of Einstein metrics on manifolds with corner and with finite boundary, showing that such metrics cannot have smooth compactifications for generic corners embedded in the infinite boundary. After that, the author studies the following. A formal expansion at the corner is derived for eigenfunctions of the scalar Laplacian subject to certain boundary conditions. Also, some important properties of the Einstein metrics are studied. Finally, it is proved that in the special case when the finite boundary is taken to be totally geodesic, there is an obstruction to existence beyond this order, which defines a conformal hypersurface invariant. In conclusion, the paper is interesting and the author presents nice and important results in the study of Einstein metrics.