In this paper, it is shown that a weakly non-decreasable dilatation in an infinitesimal Teichm\"uller equivalence class can be not a non-decreasable one. As an application, we prove that if an infinitesimal equivalence class contains more than one extremal dilatation, then it contains infinitely many weakly non-decreasable extremal dilatations.

Non-uniqueness of infinitesimally weakly non-decreasable extremal dilatations

Z. Zhou et al. proved that in a Teichmuller equivalence class, there exists an extremal quasiconformal mapping with a weakly non-decreasable dilatation. In this paper, we prove that in an infinitesimal equivalence class, there exists a weakly non-decreasable extremal Beltrami differential.

On infinitesimally weakly non-decreasable Beltrami differentials

Z Zhou et al proved that in a Teichmuller equivalence class, there exists an extremal quasiconformal mapping with a weakly non-decreasable dilatation In this paper, we prove that in an infinitesimal equivalence class, there exists a weakly non-decreasable extremal Beltrami differential

Let Q(Δ) be the set of all integrable holomorphic quadratic differentials on the unit disk Δ. The subset Q0(Δ) of Q(Δ) is the set associated with T0 classes in the universal Teichmuller space T(Δ). In this paper, it is shown that Q0(Δ) is dense in Q(Δ). The infinitesimal version is also obtained.

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Guowu Yao

Papers

On infinitesimally weakly non-decreasable Beltrami differentials

On infinitesimally weakly non-decreasable Beltrami differentials

A note on holomorphic quadratic differentials on the unit disk