##### Venue: Lecture Hall - III, Dept. of Mathematics

For a noncompact complete and simply connected harmonic manifold M, we prove the analyticity of Busemann functions on M. This is the main result of this paper. An application of it shows that the harmonic spaces having minimal horospheres have the bi-asymptotic property. Finally we prove that the total Busemann function is continuous in C^\\infty topology. As a consequence of it we show that the uniform divergence of geodesics holds in these spaces.

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Last updated: 06 Mar 2020