Nonpositively curved surfaces in \(\mathbb R^ 3\). (English) Zbl 1041.53001

Chan, Hsungrow; Treibergs, Andrejs

J. Differ. Geom. 57, No. 3, 389-407 (2001).

Let \(M\) be a \(C^2\)-regular surface immersed in \(\mathbb R^3\), which consists of one embedded connected component outside a compact set. The authors prove that if \(M\) has non-positive Gaussian curvature and a square integrable second fundamental form, then \(M\) lies between two parallel planes of \(\mathbb R^3\).

Reviewer: Bang-yen Chen (East Lansing)

MSC:

53A05

Surfaces in Euclidean and related spaces

Keywords:

nonpositive curved surface; square integrable