Convex domains of Finsler and Riemannian manifolds

Abstract

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.

22 pages, AMSLaTex. Typos corrected, references updated

References in corpus (2)

• On the energy functional on Finsler manifolds and applications to stationary spacetimes
• Global Structure of Locally Convex Hypersurfaces in Finsler-Hadamard Manifolds

Cited by in corpus (10)

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• Finsler metrics and relativistic spacetimes
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• A foliated and reversible Finsler manifold is determined by its broken scattering relation
• Convex regions of stationary spacetimes and Randers spaces. Applications to lensing and asymptotic flatness
• Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold
• Determination of a compact Finsler manifold from its boundary distance map and an inverse problem in elasticity
• An account on links between Finsler and Lorentz Geometries for Riemannian Geometers
• A sharp lower bound for the first eigenvalue on Finsler manifolds
• Brake orbits for Hamiltonian systems of classical type via Finsler geodesics