Abstract
In this paper, we consider complete hypersurfaces in R n+1 with constant mean curvature H and prove that M n is a hyperplane if the L 2 norm curvature of M n satisfies some growth condition and M n is stable. It is an improvement of a theorem proved by H. Alencar and M. do Carmo in 1994. In addition, we obtain that M n is a hyperplane (or a round sphere) under the condition that M n is strongly stable (or weakly stable) and has some finite L p norm curvature.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
