Geometric Methods in Holomorphic Dynamics

The paper explicitly states Theorem 1.1: if T is a strongly approximable geometric (1,1)-current in Ω ⊂ C^2 and S is a positive closed (1,1)-current with either bounded potentials or such that T∧S does not charge pluripolar sets, then T ∧ S is semi-geometric (see the definitions preceding (1.4) and Theorem 1.1) . The candidate’s solution follows the same established strategy: approximate T by uniformly geometric currents T^r with M(T−T^r)=O(r^2), use the geometric/leafwise wedge description (the semi-geometric formula (1.4)) and monotone convergence for bounded potentials, then treat unbounded potentials by truncation and the no-mass-on-pluripolar-sets hypothesis. These steps match the framework laid out in the survey around (1.3)–(1.4) and the strong approximability discussion (including the O(r^2) estimate obtained via cube subdivisions and projections) . The paper is a survey and does not supply a full proof on site, but it cites the correct sources; the candidate provides a coherent proof sketch in line with those references.