Heat equation and ergodic theorems for Riemann surface laminations

DOI10.1007/S00208-011-0730-8zbMATH Open1331.37064arXiv1004.3931OpenAlexW1637441234MaRDI QIDQ453325

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Publication date: 19 September 2012

Published in: (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1004.3931

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