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For $f$ geodesically convex with $L$-Lipschitz-gradient on hyperbolic space, is $f(x)-f(x^*)\leq(\mathrm{const}) \cdot L r$ for all $x \in B(x^*, r)$?
$\DeclareMathOperator\dist{dist}$Setting: Let $M$ be a hyperbolic space of sectional curvature $-1$, and let $f \colon M\to \mathbb{R}$ be a $C^2$, geodesically convex function which has $L$-Lipschitz-...
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Maximal geodesically convex function interpolating three points on the hyperbolic plane
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. ...
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