Height estimate for special Weingarten surfaces of elliptic type in ??2(??)×?

摘要

In this article we provide a vertical height estimate for compact special Weingarten surfaces of elliptic type in , i.e. surfaces whose mean curvature and extrinsic Gauss curvature satisfy with for all The vertical height estimate generalizes a result by Rosenberg and Sa Earp and applies only to surfaces verifying a height estimate condition. When using also a horizontal height estimate, we show a non-existence result for properly embedded Weingarten surfaces of elliptic type in with finite topology and one end.