ASYMPTOTIC TOTAL GEODESY OF LOCAL HOLOMORPHIC CURVES EXITING A BOUNDED SYMMETRIC DOMAIN AND APPLICATIONS TO A UNIFORMIZATION PROBLEM FOR ALGEBRAIC SUBSETS
文献类型：期刊论文
| 作者 | Chan, Shan Tai1; Mok, Ngaiming |
| 刊名 | JOURNAL OF DIFFERENTIAL GEOMETRY
 |
| 出版日期 | 2022 |
| 卷号 | 120期号:1页码:1-49 |
| ISSN号 | 0022-040X |
| 英文摘要 | The current article stems from our study on the asymptotic behavior of holomorphic isometric embeddings of the Poincare disk into bounded symmetric domains. As a first result we prove that any holomorphic curve exiting the boundary of a bounded symmetric domain Omega must necessarily be asymptotically totally geodesic. Assuming otherwise we derive by the method of rescaling a hypothetical holomorphic isometric embedding of the Poincare disk with Aut(Omega')-equivalent tangent spaces into a tube domain Omega' subset of Omega and derive a contradiction by means of the Poincare-Lelong equation. We deduce that equivariant holomorphic embeddings between bounded symmetric domains must be totally geodesic. Furthermore, we solve a uniformization problem on algebraic subsets Z subset of Omega. More precisely, if (Gamma) over cap subset of Aut(Omega) is a torsion-free discrete subgroup leaving Z invariant such that Z=(Gamma) over cap is compact, we prove that Z subset of Omega is totally geodesic. In particular, letting Gamma subset of Aut(Omega) be a torsion-free cocompact lattice, and pi : Omega -> Omega/Gamma =: X-Gamma be the uniformization map, a subvariety Y subset of X-Gamma must be totally geodesic whenever some (and hence any) irreducible component Z of pi(-1) (Y) is an algebraic subset of Omega. For cocompact lattices this yields a characterization of totally geodesic subsets of X-Gamma by means of bi-algebraicity without recourse to the celebrated monodromy result of Andre-Deligne on subvarieties of Shimura varieties, and as such our proof applies to not necessarily arithmetic cocompact lattices. In place of the monodromy result of Andre-Deligne we exploit the existence theorem of Aubin and Yau on Kahler-Einstein metrics for projective manifolds Y satisfying c(1)(Y) < 0 and make use of Nadel's semisimplicity theorem on automorphism groups of noncompact Galois covers of such manifolds, together with the total geodesy of equivariant holomorphic isometric embeddings between bounded symmetric domains. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| 出版者 | INT PRESS BOSTON, INC |
| WOS记录号 | WOS:000743374700001 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59886]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Chan, Shan Tai |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China 2.Univ Hong Kong, Dept Math, Pokfulam Rd, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Chan, Shan Tai,Mok, Ngaiming. ASYMPTOTIC TOTAL GEODESY OF LOCAL HOLOMORPHIC CURVES EXITING A BOUNDED SYMMETRIC DOMAIN AND APPLICATIONS TO A UNIFORMIZATION PROBLEM FOR ALGEBRAIC SUBSETS[J]. JOURNAL OF DIFFERENTIAL GEOMETRY,2022,120(1):1-49. |
| APA | Chan, Shan Tai,&Mok, Ngaiming.(2022).ASYMPTOTIC TOTAL GEODESY OF LOCAL HOLOMORPHIC CURVES EXITING A BOUNDED SYMMETRIC DOMAIN AND APPLICATIONS TO A UNIFORMIZATION PROBLEM FOR ALGEBRAIC SUBSETS.JOURNAL OF DIFFERENTIAL GEOMETRY,120(1),1-49. |
| MLA | Chan, Shan Tai,et al."ASYMPTOTIC TOTAL GEODESY OF LOCAL HOLOMORPHIC CURVES EXITING A BOUNDED SYMMETRIC DOMAIN AND APPLICATIONS TO A UNIFORMIZATION PROBLEM FOR ALGEBRAIC SUBSETS".JOURNAL OF DIFFERENTIAL GEOMETRY 120.1(2022):1-49. |
入库方式： OAI收割
来源：数学与系统科学研究院
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