HEIGHT ESTIMATE FOR SPECIAL WEINGARTEN SURFACES OF ELLIPTIC TYPE IN M(c)× R
نویسندگان
چکیده
In this article we provide a vertical height estimate for compact special Weingarten surfaces of elliptic type in M2(c) × R, i.e. surfaces whose mean curvature H and extrinsic Gauss curvature Ke satisfy H = f(H2 −Ke) with 4x(f ′(x))2 < 1, for all x ∈ [0,+∞). The vertical height estimate generalizes a result by Rosenberg and Sa Earp and applies only to surfaces verifying a height estimate condition. When c < 0, using also a horizontal height estimate, we show a non-existence result for properly embedded Weingarten surfaces of elliptic type in H2(c)× R with finite topology and one end.
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