The Bernstein conjecture, minimal cones and critical dimensions

@article{Gibbons2009TheBC,
  title={The Bernstein conjecture, minimal cones and critical dimensions},
  author={G. W. Gibbons and Kei-ichi Maeda and Umpei Miyamoto},
  journal={Classical and Quantum Gravity},
  year={2009},
  volume={26},
  pages={185008}
}
Minimal surfaces and domain walls play important roles in various contexts of spacetime physics as well as material science. In this paper, we first review the Bernstein conjecture, which asserts that a plane is the only globally well-defined solution of the minimal surface equation which is a single valued graph over a hyperplane in flat spaces, and its failure in higher dimensions. Then, we review how minimal cones in four- and higher-dimensional spacetimes, which are curved and even singular… 

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