Height estimate for special Weingarten surfaces of elliptic type in ${\mathbb M}^2(c) \times \mathbb {R}$
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- by Filippo Morabito HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 1 (2014), 14-22
Abstract:
In this article we provide a vertical height estimate for compact special Weingarten surfaces of elliptic type in ${\mathbb M}^2(c) \times \mathbb {R}$, i.e. surfaces whose mean curvature $H$ and extrinsic Gauss curvature $K_e$ satisfy $H=f(H^2-K_e)$ with $4x(f’(x))^2<1,$ for all $x \in [0,+\infty ).$ 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 $\mathbb {H}^2(c) \times \mathbb {R}$ with finite topology and one end.References
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Additional Information
- Filippo Morabito
- Affiliation: Korea Institute for Advanced Study, Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, South Korea
- Address at time of publication: Department of Mathematical Sciences, Korea Advanced Institute Science Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, South Korea
- MR Author ID: 864654
- Received by editor(s): July 31, 2011
- Received by editor(s) in revised form: June 20, 2012, January 29, 2013, March 29, 2013, and April 3, 2013
- Published electronically: January 10, 2014
- Communicated by: Michael Wolf
- © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 14-22
- MSC (2010): Primary 53A10
- DOI: https://doi.org/10.1090/S2330-1511-2014-00005-5
- MathSciNet review: 3148816