2010/04/22 by Tien-Cuong Dinh, Tien‐Cuong Dinh, Viet-Anh Nguyen +5
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #math.DS #msc:37A #msc:37F75
paper · pdf · doi:10.48550/arxiv.1004.3931
44 pages
arxiv created 2010/04/22 · arxiv updated 2010/04/23
We introduce the heat equation relative to a positive dd-bar-closed current and apply it to the invariant currents associated with Riemann surface laminations possibly with singularities. The main examples are holomorphic foliations by Riemann surfaces in projective spaces. We prove two kinds of ergodic theorems for such currents: one associated to the heat diffusion and one close to Birkhoff's averaging on orbits of a dynamical system. The heat diffusion theorem with respect to a harmonic measure is also developed for real laminations.