Abstract
Abstract
We prove that any metric with curvature less than or equal to
$-1$
(in the sense of A. D. Alexandrov) on a closed surface of genus greater than
$1$
is isometric to the induced intrinsic metric on a space-like convex surface in a Lorentzian manifold of dimension
$(2+1)$
with sectional curvature
$-1$
. The proof is by approximation, using a result about isometric immersion of smooth metrics by Labourie and Schlenker.
Publisher
Cambridge University Press (CUP)
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