On the existence of convex functions on Finsler manifolds

2018/11/06 by Sabau, Sorin V., Chansangiam, Pattrawut
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.02121

Abstract

We show that a non-compact (forward) complete Finsler manifold whose Holmes- Thompson volume is infinite admits no non-trivial convex functions. We apply this result to some Finsler manifolds whose Busemann function is convex.

Related

• Topology of complete Finsler manifolds admitting convex functions
• Convexity and some geometric properties
• Convex Neighbourhoods and Complete Finsler Spaces
• Convexity on Manifolds without Focal points and applications
• The global study of Riemannian-Finsler geometry