LOCAL PRODUCT STRUCTURE FOR EQUILIBRIUM STATES OF GEODESIC FLOWS AND APPLICATIONS

The paper proves (i) local product structure on sets of arbitrarily large measure for equilibrium states of Hölder potentials locally constant near Sing, (ii) Bernoulli property for all time-t maps, and (iii) a global Bowen property for such potentials. The candidate solution follows the same CCESW framework: Climenhaga–Thompson decomposition with a pressure gap, upgrade to a global Bowen property, derive local product structure, and apply Ornstein–Weiss to obtain Bernoulli. The only notable mismatch is that the model briefly overstates the lower Gibbs property as uniform on all Bowen balls, whereas the paper retains a non-uniform lower Gibbs bound tied to regularity via λ. This does not affect the core conclusions.