The eventually distance minimizing ray（EDM ray） in moduli spaces of the Riemann surfaces of analytic finite type with 3 g ＋ n-3 〉 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance o...The eventually distance minimizing ray（EDM ray） in moduli spaces of the Riemann surfaces of analytic finite type with 3 g ＋ n-3 〉 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmu¨ller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given.展开更多
In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimens...In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P（Dn, BN） is C1＋α at z0 ∈ ErDn with f（0） = 0 and f（z0） = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =（λ1,0,…,λr,0,…,0）T∈R2 nsatisfying λi≥1/（22 n-1） for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.展开更多
基金supported by the National Natural Science Foundation of China(11371045)
文摘The eventually distance minimizing ray（EDM ray） in moduli spaces of the Riemann surfaces of analytic finite type with 3 g ＋ n-3 〉 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmu¨ller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given.
基金Supported by the Natural and Science Foundation of China(61379001,61771001)
文摘In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P（Dn, BN） is C1＋α at z0 ∈ ErDn with f（0） = 0 and f（z0） = ω0∈BN for any n,N ≥ 1, then there exist a nonnegative vector λf =（λ1,0,…,λr,0,…,0）T∈R2 nsatisfying λi≥1/（22 n-1） for 1 ≤ i ≤ r such that where z’0 and w’0 are real versions of z0 and w0, respectively.
