From metric properties to a rigidity conjecture on Finsler manifolds via a geodesic detecting algorithm
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The aim of this note and video clips is to consider Busemann-type inequalities on Finsler manifolds. We actually formulate a rigidity conjecture: any Finsler manifold which is a Busemann NPC space is Berwaldian. This statement is supported by some theoretical results and numerical examples. The presented examples are obtained by using evolutionary techniques (genetic algorithms) which can be used for detecting geodesics on a large class of not necessarily reversible Finsler manifolds.
Remark
Due to the huge size of the attached high resolution avi files we needed to use the 7-zip file archiver that has a high compression ratio. We kindly suggest to use a better avi file player like the SMPlayer. (Both applications are free to download and use.)
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