A note on Hamilton sequences of extremal Beltrami differentials

Let X be a hyperbolic Riemann surface and let μ be an extremal Beltrami differential on X with ‖μ‖∞∈(0,1). It is proved that, if {ϕn} is a Hamilton sequence of μ, then {ϕn} must be a Hamilton sequence of any extremal Beltrami differential ν contained in [μ]. This result proved a conjecture of the first author of this paper in 1996. This result is also a generalization of two known results.