<ul><li>This article presents three isometric models of the Funk disc: the Finsler upper half of the hyperboloid of two sheets model, Finsler band model, and Finsler upper hemi sphere model.</li><li>Two new models of the Finsler-Poincaré disc are also introduced.</li><li>The geodesics in each model are explicitly described.</li><li>The Busemann function and horocycles in the Funk and Hilbert disc are computed and described.</li><li>Additionally, the article proves the asymptotic harmonicity of the Funk disc. It is demonstrated that the concept of asymptotic harmonicity in Finsler manifolds depends on the measure, contrasting the Riemannian case.</li><li>Another article by Jiayin Pan and Guofang Wei provides the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function at a point. This counters the well-known open question regarding the properness of Busemann functions on open manifolds with nonnegative Ricci curvature.</li></ul>

Working with Busemann functions part2(Machine Learning 2024)

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