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A Tzitzeica surface has the property that the ratio of the surface’s Gaussian curvature and the fourth power of the distance from the origin to the tangent plane at any arbitrary point of the surface ...

Crossposted on MSE: https://math.stackexchange.com/questions/4282998/maximal-geodesically-convex-function-interpolating-three-points-on-the-hyperboli Let $M$ be a two-dimensional Hadamard manifold. ...

A famous theorem of Birman and Series says that if $S$ is a compact hyperbolic surface, then the set of points that lie on simple geodesics is nowhere dense and has Hausdorff dimension one; in ...