#### Vol. 276, No. 2, 2015

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Isometric embedding of negatively curved complete surfaces in Lorentz–Minkowski space

### Bing-Long Chen and Le Yin

Vol. 276 (2015), No. 2, 347–367
##### Abstract

The Hilbert–Efimov theorem states that any complete surface with curvature bounded above by a negative constant cannot be isometrically embedded in ${ℝ}^{\mathfrak{3}}$. We demonstrate that any simply connected smooth complete surface with curvature bounded above by a negative constant admits a smooth isometric embedding into the Lorentz–Minkowski space ${ℝ}^{\mathfrak{2},\mathfrak{1}}$.

##### Keywords
isometric embedding, Hilbert–Efimov theorem, Lorentz–Minkowski space
Primary: 53C21
Secondary: 35J96