Skip to main content
Became Hot Network Question
edited tags
Link
Anton Petrunin
  • 47k
  • 17
  • 145
  • 312
Source Link
Sean
  • 339
  • 1
  • 6

Stable minimal surface whose Gauss curvature is not everywhere positive

Let $(M, g)$ be a 3-dimensional Riemannian manifold with positive scalar curvature, and let $\Sigma\subset M$ be a compact minimal surface without boundary. It is known that (e.g. by the work of Schoen and Yau) if $\Sigma$ is stable, then the integral of Gauss curvature $\int_\Sigma K_\Sigma\ge 0$. What are examples of $(M,g)$ that contain a stable minimal surface with negative Gauss curvature somewhere?