For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence...For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.展开更多
The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrig...The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.展开更多
An explicit example of a Reich sequence for a uniquely extremal quasiconformal mapping in a borderline case between uniqueness and non-uniqueness is given.
文摘For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.
基金Supported by the National Natural Science Foundation of China(10671174, 10401036)a Foundation for the Author of National Excellent Doctoral Dissertation of China(200518)
文摘The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.
文摘An explicit example of a Reich sequence for a uniquely extremal quasiconformal mapping in a borderline case between uniqueness and non-uniqueness is given.
