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Daryl Cooper
Daryl Cooper
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For complete Riemannian manifolds of bounded sectional curvature the answer is YES by L.F. Tam. Exhaustion functions on complete manifolds on complete manifolds* MR2648946. Then the answer for the Hilbert metric on a properly convex manifold is also YES since such a manifold admits a Riemannian metric of bounded curvature that is bi-Lipshitz to the Hilbert metric

For complete Riemannian manifolds of bounded sectional curvature the answer is YES by L.F. Tam. Exhaustion functions on complete manifolds* MR2648946. Then the answer for the Hilbert metric on a properly convex manifold is also YES since such a manifold admits a Riemannian metric of bounded curvature that is bi-Lipshitz to the Hilbert metric

For complete Riemannian manifolds of bounded sectional curvature the answer is YES by L.F. Tam. Exhaustion functions on complete manifolds MR2648946. Then the answer for the Hilbert metric on a properly convex manifold is also YES since such a manifold admits a Riemannian metric of bounded curvature that is bi-Lipshitz to the Hilbert metric

Source Link
Daryl Cooper
Daryl Cooper
  • 700
  • 4
  • 11

For complete Riemannian manifolds of bounded sectional curvature the answer is YES by L.F. Tam. Exhaustion functions on complete manifolds* MR2648946. Then the answer for the Hilbert metric on a properly convex manifold is also YES since such a manifold admits a Riemannian metric of bounded curvature that is bi-Lipshitz to the Hilbert metric