TY - JOUR
T1 - Lyapunov exponents of the Brownian motion on a Kähler manifold
AU - Daniel, Jeremy
AU - Deroin, Bertrand
N1 - Publisher Copyright:
© 2019 International Press of Boston, Inc.. All rights reserved.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - If E is a flat bundle of rank r over a Kähler manifold X, we define the Lyapunov spectrum of E: a set of r numbers controlling the growth of flat sections of E, along Brownian trajectories. We show how to compute these numbers, by using harmonic measures on the foliated space P(E). Then, in the case where X is compact, we prove a general inequality relating the Lyapunov exponents and the degrees of holomorphic subbundles of E and we discuss the equality case.
AB - If E is a flat bundle of rank r over a Kähler manifold X, we define the Lyapunov spectrum of E: a set of r numbers controlling the growth of flat sections of E, along Brownian trajectories. We show how to compute these numbers, by using harmonic measures on the foliated space P(E). Then, in the case where X is compact, we prove a general inequality relating the Lyapunov exponents and the degrees of holomorphic subbundles of E and we discuss the equality case.
U2 - 10.4310/MRL.2019.v26.n2.a6
DO - 10.4310/MRL.2019.v26.n2.a6
M3 - Article
AN - SCOPUS:85072636454
SN - 1073-2780
VL - 26
SP - 501
EP - 536
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 2
ER -