REVIEW 1 cited by
Hypersurfaces of constant scalar curvature in hyperbolic space with prescribed asymptotic boundary at infinity
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
This article concerns a natural generalization of the classical asymptotic Plateau problem in hyperbolic space. We prove the existence of a smooth complete hypersurface of constant scalar curvature with a prescribed asymptotic boundary at infinity. The desired hypersurface is constructed as the limit of constant scalar curvature graphs (with respect to vertical geodesics) over a fixed compact domain in a horosphere, and the problem is thus reduced to solving a Dirichlet problem for a fully nonlinear elliptic partial differential equation which is degenerate along the boundary. Previously, the result was known only for a restricted range of curvature values. Now, in this article, by introducing some new techniques, we are able to solve the Dirichlet problem for all possible curvature values. The main ingredient is the establishment of the crucial second order a priori estimates for admissible solutions.
Forward citations
Cited by 1 Pith paper
-
Hypersurfaces of constant sum Hessian curvature in Hyperbolic space
For the constant sum Hessian curvature equation in hyperbolic space, a curvature estimate and conditional existence are proved under an extra lower-bound assumption on sigma_n; the unconditional problem remains open.
Discussion (0). Sign in to comment.