About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 315768, 7 pages
http://dx.doi.org/10.1155/2014/315768
Research Article

Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone

School of Mathematics and Statistics, Hubei University, Wuhan 430062, China

Received 9 January 2014; Accepted 30 June 2014; Published 17 July 2014

Academic Editor: Narcisa C. Apreutesei

Copyright © 2014 Fangcheng Guo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Guan and J. Li, “A mean curvature type flow in space forms,” International Mathematics Research Notices, 2014. View at Publisher · View at Google Scholar
  2. G. Huisken, “Nonparametric mean curvature evolution with boundary conditions,” Journal of Differential Equations, vol. 77, no. 2, pp. 369–378, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. A. Stahl, “Convergence of solutions to the mean curvature flow with a Neumann boundary condition,” Calculus of Variations and Partial Differential Equations, vol. 4, no. 5, pp. 421–441, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. A. Stahl, “Regularity estimates for solutions to the mean curvature flow with a Neumann boundary condition,” Calculus of Variations and Partial Differential Equations, vol. 4, no. 4, pp. 385–407, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. J. A. Buckland, “Mean curvature flow with free boundary on smooth hypersurfaces,” Journal für die Reine und Angewandte Mathematik, vol. 586, pp. 71–90, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. B. Lambert, “The perpendicular Neumann problem for mean curvature flow with a timelike cone boundary condition,” Transactions of the American Mathematical Society, vol. 366, no. 7, pp. 3373–3388, 2014. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. B. Lambert, “The constant angle problem for mean curvature flow inside rotational tori,” http://arxiv.org/abs/1207.4422.
  8. D. Hartley, “Motion by volume preserving mean curvature flow near cylinders,” Communications in Analysis and Geometry, vol. 21, no. 5, pp. 873–889, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. J. Altschuler and L. F. Wu, “Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle,” Calculus of Variations and Partial Differential Equations, vol. 2, no. 1, pp. 101–111, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. B. Guan, “Mean curvature motion of non-parametric hypersurfaces with contact angle condition,” in Elliptic and Parabolic Methods in Geometry, pp. 47–56, A. K. Peters, Wellesley, Mass, USA, 1996.
  11. G. Li and I. Salavessa, “Forced convex mean curvature flow in Euclidean spaces,” Manuscripta Mathematica, vol. 126, no. 3, pp. 333–351, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. X. Zhu, Lectures on Mean Curvature Flows, vol. 32 of Studies on Advanced Mathematics, American Mathematical Society, International Press, 2002. View at MathSciNet
  13. G. Lieberman, Second Order Parabolic Differential Equations, World Scientific Publishing, 1996.
  14. K. Ecker and G. Huisken, “Mean curvature evolution of entire graphs,” Annals of Mathematics, vol. 130, no. 3, pp. 453–471, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  15. M. Protter and H. Weinberger, Maximum Principle in Differential Equation, Springer, 1984.