Global Structure of Locally Convex Hypersurfaces in Finsler-Hadamard Manifolds

TL;DR

This paper investigates the global structure of locally convex hypersurfaces in Finsler-Hadamard manifolds with bounded T-curvature, proving they form the boundary of convex bodies under specific curvature conditions.

Contribution

It establishes conditions under which locally convex hypersurfaces in Finsler-Hadamard manifolds are embedded as convex boundaries, extending convexity results to Finsler geometry.

Findings

Hypersurfaces are embedded as convex bodies under certain curvature bounds.

Conditions on normal curvatures ensure the hypersurfaces are boundaries of convex sets.

Results generalize convexity properties from Riemannian to Finsler-Hadamard manifolds.

Abstract

Locally convex compact immersed hypersurfaces in Finsler-Hadamard manifolds with bounded T-curvature are considered. We prove that such hypersurfaces are embedded as the boundary of convex body under certain conditions on the normal curvatures