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Heat equation and ergodic theorems for Riemann surface laminations by Dinh, Tien-Cuong; Nguyen, Viet-Anh; Sibony, Nessim is a scholarly article available to read on EtoBox.

What is Heat equation and ergodic theorems for Riemann surface laminations about?

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.

Author

Dinh, Tien-Cuong; Nguyen, Viet-Anh; Sibony, Nessim

Published

2010

Language

EN