Let (X,D) be a log smooth log canonical pair such that K_X+D is ample. Extending a theorem of Guenancia and building on his techniques, we show that negatively curved Kahler-Einstein crossing edge metrics converge to Kahler-Einstein mixed cusp and edge metrics smoothly away from the divisor when some of the cone angles converge to 0. We further show that near the divisor such normalized Kahler-Einstein crossing edge metrics converge to a mixed cylinder and edge metric in the pointed Gromov-Hausdorff sense when some of the cone angles converge to 0 at (possibly) different speeds.

Research supported in part by the NSF grant DMS-1906370 and the Michael Brin Graduate Fellowship at the University of Maryland.