Pan–Rong conjecture in dimensions above five

Establish finite generation of the fundamental group of every open complete n-manifold with nonnegative Ricci curvature whose universal cover has Euclidean volume growth, for dimensions not covered by the dimension-five result, thereby resolving the remaining cases of the Pan–Rong conjecture.

Background

The paper studies the Pan–Rong conjecture, which asserts that the fundamental group of an open n-manifold with nonnegative Ricci curvature and Euclidean volume growth on its universal cover is finitely generated. The paper proves the conjecture in dimension five and notes that the general higher-dimensional case remains unresolved.