Projections of Gibbs measures on self-conformal sets

Hochman and Shmerkin used Furstenberg’s theory of CP-processes to prove strong Marstrand results for self-similar sets and measures with dense rotations which satisfy the strong separation condition. That is, to prove that the Hausdorff dimension of the projections of such sets and measures is the maximum possible value for every projection. Here we extend such a result to Gibbs measures on self-conformal sets without requiring any separation condition. The extension relies on some careful estimates of the entropy growth of non-linearly zoomed-in measures and the distortion of conformal iterated function systems under orthogonal projections. The result applies to Gibbs measures on hyperbolic Julia sets.