Since we know that $\mathbb{H}^{2} \times \mathbb{H}^{2}$ is Hadamard manifold. It is written in the paper " Equidistance surface of the bidisc" that $\textbf{Every sphere bounds a ball that is strictly convex}$. Can someone explains me whether it is property of Hadamard manifold or it is some theorem about Hadamard manifold.
Properties of Hadamard Manifold
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geometry
riemannian-geometry
hyperbolic-geometry
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0Have a look at "Convex sets in Hadamard manifolds" by A.A Borisenko Differential Geometry and its Applications Volume 17, Issues 2–3, September 2002, Pages 111–121 (http://www.sciencedirect.com/science/article/pii/S092622450200102X) – 2017-01-10