Manifolds with sublinear volume growth admit bounded mean-concave exhaustions and those with infinitely many ends have escaping geodesics, enabling curvature-free proofs of classical volume and ends theorems.
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Curvature-free effects from volume growth and ends-counting and their applications
Manifolds with sublinear volume growth admit bounded mean-concave exhaustions and those with infinitely many ends have escaping geodesics, enabling curvature-free proofs of classical volume and ends theorems.