We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi＇s metric and Teichmuller＇s metric coincide with each other on the Teichmfiller space of symmetric circle homeomorphisms.
Let B2,p :={z∈C2 :|z1|^2 +|z2|^p < 1}(0 < p < 1). Then, B2,p (0 < p < 1) is a non-convex complex ellipsoid in C2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈...Let B2,p :={z∈C2 :|z1|^2 +|z2|^p < 1}(0 < p < 1). Then, B2,p (0 < p < 1) is a non-convex complex ellipsoid in C2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈B2,p for holomorphic self-mappings of the non-convex complex ellipsoid ￡2?, where zq is any smooth boundary point of B2,p.展开更多
Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius tran...Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.展开更多
In this paper we show that the Kobayashi-Royden metric and the Sibony metric are different on ring domains,i.e.,the difference of two concentric balls,in higher dimension.
In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary.The strategy is t...In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary.The strategy is to reestablish the Gehring-Hayman-type Theorem for these complex domains.Furthermore,the regularity of boundary extension map is given.展开更多
In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
For a class of Reinhardt domains, we prove that the holomorphic sectional curvatures are upper-bounded by a negative constant. Then we obtain a comparison theorem for the Kobayashi and Bergman metrics on the domains.
In this paper, we investigate rigidity and its applications to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounde...In this paper, we investigate rigidity and its applications to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounded convex mappings with only one in?nite discontinuity on the boundary of this domain. We also give a rigidity of these unbounded convex mappings via the Kobayashi metric and the Liouville-type theorem of entire functions. As an application we obtain a collection of extreme points for the class of normalized convex mappings. Our results extend both the rigidity of convex mappings and related extreme points from the unit ball to Reinhardt domains.展开更多
文摘We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi＇s metric and Teichmuller＇s metric coincide with each other on the Teichmfiller space of symmetric circle homeomorphisms.
基金The project supported in part by the National Natural Science Foundation of China(11671306)
文摘Let B2,p :={z∈C2 :|z1|^2 +|z2|^p < 1}(0 < p < 1). Then, B2,p (0 < p < 1) is a non-convex complex ellipsoid in C2 without smooth boundary. In this article, we establish a boundary Schwarz lemma at z0 ∈B2,p for holomorphic self-mappings of the non-convex complex ellipsoid ￡2?, where zq is any smooth boundary point of B2,p.
基金supported by the National Science Foundationsupported by a collaboration grant from the Simons Foundation(Grant No.523341)PSC-CUNY awards and a grant from NSFC(Grant No.11571122)。
文摘Given a modulus of continuity ω,we consider the Teichmuller space TC1+ω as the space of all orientation-preserving circle diffeomorphisms whose derivatives are ω-continuous functions modulo the space of Mobius transformations preserving the unit disk.We study several distortion properties for diffeomorphisms and quasisymmetric homeomorphisms.Using these distortion properties,we give the Bers complex manifold structure on the Teichm(u| ")ller space TC^1+H as the union of over all0 <α≤1,which turns out to be the largest space in the Teichmuller space of C1 orientation-preserving circle diffeomorphisms on which we can assign such a structure.Furthermore,we prove that with the Bers complex manifold structure on TC^1+H ,Kobayashi’s metric and Teichmuller’s metric coincide.
基金supported by National Science Foundation (Grant No. DMS 0705027)
文摘In this paper we show that the Kobayashi-Royden metric and the Sibony metric are different on ring domains,i.e.,the difference of two concentric balls,in higher dimension.
基金supported by National Key R&D Program of China(Grant No.2021YFA1003100)NSFC(Grant Nos.11925107 and 12226334)+2 种基金Key Research Program of Frontier Sciences,CAS(Grant No.ZDBS-LY-7002)supported by the Young Scientist Program of the Ministry of Science and Technology of China(Grant No.2021YFA1002200)NSFC(Grant No.12201059)。
文摘In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is infinitely flat extend continuously to the boundary.The strategy is to reestablish the Gehring-Hayman-type Theorem for these complex domains.Furthermore,the regularity of boundary extension map is given.
文摘In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
基金Project supported partly by the National Natural Science Foundation of China
文摘For a class of Reinhardt domains, we prove that the holomorphic sectional curvatures are upper-bounded by a negative constant. Then we obtain a comparison theorem for the Kobayashi and Bergman metrics on the domains.
基金supported by National Natural Science Foundation of China (Grant Nos. 11471111, 11571105 and 11671362)the Natural Science Foundation of Zhejiang Province (Grant No. LY16A010004)
文摘In this paper, we investigate rigidity and its applications to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounded convex mappings with only one in?nite discontinuity on the boundary of this domain. We also give a rigidity of these unbounded convex mappings via the Kobayashi metric and the Liouville-type theorem of entire functions. As an application we obtain a collection of extreme points for the class of normalized convex mappings. Our results extend both the rigidity of convex mappings and related extreme points from the unit ball to Reinhardt domains.
