Skip to main content
Article thumbnail
Location of Repository

Maximal Graphs and Spacelike Mean Curvature Flows in Semi-Euclidean Spaces

By STUART BENJAMIN THORPE

Abstract

Two main results are proved. The first is for the maximal graph system in semi-Euclidean spaces. Existence of smooth solutions to the Dirichlet problem is proved, under certain assumptions on the boundary data. These assumptions allow the application of standard elliptic PDE methods by providing sufficiently strong a priori gradient estimates. The second result is a version of Brian White’s local regularity theorem, but now for the spacelike mean curvature flow system in semi-Euclidean spaces. This is proved using a version of Huisken’s monotonicity formula. Under the assumption of a suitable gradient bound, this theorem will give a priori estimates that allow such flows to be smoothly extended locally

Year: 2011
OAI identifier: oai:etheses.dur.ac.uk:711
Provided by: Durham e-Theses

Suggested articles

Citations

  1. (2005). A Local Regularity Theorem for Mean Curvature Flow, doi
  2. (1990). Asymptotic Behaviour for Singularities of the Mean Curvature Flow, doi
  3. (1989). Direct Methods in the Calculus of Variations, doi
  4. (1998). Elliptic Partial Differential Equations of Second Order, doi
  5. (2009). Graphic Bernstein Results in Curved Pseudo-Riemannian Manifolds, doi
  6. (2003). Introduction to Smooth Manifolds, doi
  7. (2010). Mean Curvature Flow of Spacelike Graphs, doi
  8. (2001). Mean Curvature Flow of Surfaces in Einstein Four-Manifolds,
  9. (1977). Non-Existence, Non-Uniqueness and Irregularity of Solutions to the Minimal Surface System, doi
  10. (1966). On the Bounded Slope Condition, doi
  11. (1990). Ordinary Differential Equations: an Introduction to Nonlinear Analysis, De Gruyter, doi
  12. (1964). Partial Differential Equations of Parabolic Type, doi
  13. (2005). Postmodern Analysis (Third Edition), doi
  14. (2004). Regularity Theory for Mean Curvature Flow, Birkhauser, doi
  15. (1991). Second Order Elliptic Equations and Elliptic Systems, doi
  16. (1996). Second Order Parabolic Differential Equations, World Scientific, doi
  17. (1983). Semi-Riemannian Geometry, doi
  18. (1997). Singularities of Mean Curvature Flow of Surfaces,
  19. (1982). Spacelike Hypersurfaces with Prescribed Boundary Values and Mean Curvature, doi
  20. (1979). The Boundary Value Problem for Maximal Hypersurfaces, doi
  21. (1968). The Dirichlet Problem for the Minimal Surface Equation in Higher Dimension, doi
  22. (2004). The Dirichlet Problem for the Minimal Surface System in doi
  23. (0411). The Non-Parametric Problem of Plateau in Arbitrary Codimension,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.