Monotonicity formula for complete hypersurfaces in the hyperbolic space and applications

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• 作者：Hilário Alencar ; Gregório Silva Neto
• 刊名：Arkiv f?r Matematik
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：54
• 期：1
• 页码：1-11
• 全文大小：830 KB
• 参考文献：1. Alencar, H. , do Carmo, M. and Santos, W. , A gap theorem for hypersurfaces of the sphere with constant scalar curvature one, Comment. Math. Helv. 77 (2002), 549–562. doi:10.​1007/​s00014-002-8351-1 . MR1933789 (2003m:53098). MathSciNet CrossRef MATH
  2. Alencar, H. and Frensel, K. , Hypersurfaces whose tangent geodesics omit a nonempty set, in Differential Geometry 52, pp. 1–13, Longman Sci. Tech., Harlow, 1991. MR1173029 (93f:53048).
  3. Alencar, H. , Santos, W. , Zhou, D. , Curvature integral estimates for complete hypersurfaces, Illinois J. Math. 55 (2012), 185–203. MR3006685. MathSciNet MATH
  4. Jorge, L. and Koutroufiotis, D. , An estimate for the curvature of bounded submanifolds, Amer. J. Math. 103 (1981), 711–725. doi:10.​2307/​2374048 . MR623135 (83d:53041b). MathSciNet CrossRef MATH
  5. Reilly, R. C. , Variational properties of functions of the mean curvatures for hypersurfaces in space forms, J. Differential Geom. 8 (1973), 465–477. MR0341351 (49 #6102). MathSciNet MATH
  6. Rosenberg, H. , Hypersurfaces of constant curvature in space forms, Bull. Sci. Math. 117 (1993), 211–239. MR1216008 (94b:53097). MathSciNet MATH
  
• 作者单位：Hilário Alencar (1)
  Gregório Silva Neto (1)
  
  1. Instituto de Matemática, Universidade Federal de Alagoas, Maceió, AL, 57072-900, Brasil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1871-2487

文摘

In this paper we prove a monotonicity formula for the integral of the mean curvature for complete and proper hypersurfaces of the hyperbolic space and, as consequences, we obtain a lower bound for the integral of the mean curvature and that the integral of the mean curvature is infinity.