Busemann functions in asymptotically harmonic Finsler manifolds
Hemangi Shah, Ebtsam H. Taha
TL;DR
This paper studies Busemann functions in Finsler geometry, demonstrating their smoothness in asymptotically harmonic Finsler manifolds and expanding understanding of their geometric properties.
Contribution
It establishes the smoothness of Busemann functions specifically in asymptotically harmonic Finsler manifolds, a novel result in this geometric setting.
Findings
Busemann functions are smooth in asymptotically harmonic Finsler manifolds.
The paper extends the understanding of Busemann functions beyond Riemannian geometry.
Provides foundational results for further geometric analysis in Finsler spaces.
Abstract
In the present paper, we investigate Busemann functions in a general Finsler setting as well as in asymptotically harmonic Finsler manifolds. In particular, we show Busemann functions are smooth on asymptotically harmonic Finsler manifolds.
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Taxonomy
TopicsAdvanced Differential Geometry Research