No full text
Eprint already available on another site (E-prints, Working papers and Research blog)
The Weyl problem for unbounded convex domains in $\HH^3$
Schlenker, Jean-Marc


Full Text
No document available.

Send to


Abstract :
[en] Let $K\subset \HH^3$ be a convex subset in $\HH^3$ with smooth, strictly convex boundary. The induced metric on $\partial K$ then has curvature $K>-1$. It was proved by Alexandrov that if $K$ is bounded, then it is uniquely determined by the induced metric on the boundary, and any smooth metric with curvature $K>-1$ can be obtained. We propose here an extension of the existence part of this result to unbounded convex domains in $\HH^3$. The induced metric on $\partial K$ is then clearly not sufficient to determine $K$. However one can consider a richer data on the boundary including the ideal boundary of $K$. Specifically, we consider the data composed of the conformal structure on the boundary of $K$ in the Poincar\'e model of $\HH^3$, together with the induced metric on $\partial K$. We show that a wide range of "reasonable" data of this type, satisfying mild curvature conditions, can be realized on the boundary of a convex subset in $\HH^3$. We do not consider here the uniqueness of a convex subset with given boundary data.
Disciplines :
Author, co-author :
Schlenker, Jean-Marc ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
Title :
The Weyl problem for unbounded convex domains in $\HH^3$
Publication date :
Number of pages :
Available on ORBilu :
since 07 June 2021


Number of views
43 (0 by Unilu)
Number of downloads
0 (0 by Unilu)


Similar publications

Contact ORBilu