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?
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