The Loewner-Nirenberg problem in singular domains

摘要

We study asymptotic behaviors of solutions of the Loewner-Nirenberg problem in singular domains and prove that the solutions are well approximated by the corresponding solutions in tangent cones at singular points on the boundary. The conformal structure of the underlying equation plays an essential role in the derivation of the optimal estimates. (C) 2020 Elsevier Inc. All rights reserved.