BUNCHING FOR RELATIVELY PINCHED METRICS

The uploaded paper proves that under relative negative a^2 pinching, the horospherical foliation is C^{2a−} by deriving an averaged (periodic-orbit) inequality for the Riccati eigenvalues and invoking Hasselblatt’s criterion (see the statement of Theorem 1 and its proof outline, together with Proposition 3 and Theorem 2) . In contrast, the candidate solution hinges on a pointwise comparison λ_min(t) ≥ a λ_max(t) for the unstable Riccati operator derived directly from relative pinching of curvature; the paper explicitly notes that such a pointwise upgrade from a^2 to a is generally false (cf. the GHK obstruction) and replaces it by control of time-averaged quantities along periodic orbits . Thus, although the candidate reaches the right exponent 2a, its core argument uses an invalid step, while the paper’s proof is correct.