Skip to main content
×
Home
    • Aa
    • Aa

ALGEBRAIC CONVERGENCE THEOREMS OF COMPLEX KLEINIAN GROUPS

  • WENSHENG CAO (a1)
Abstract
Abstract

Let {Gr,i} be a sequence of r-generator subgroups of U(1,n; ℂ) and Gr be its algebraic limit group. In this paper, two algebraic convergence theorems concerning {Gr,i} and Gr are obtained. Our results are generalisations of their counterparts in the n-dimensional sense-preserving Möbius group.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      ALGEBRAIC CONVERGENCE THEOREMS OF COMPLEX KLEINIAN GROUPS
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      ALGEBRAIC CONVERGENCE THEOREMS OF COMPLEX KLEINIAN GROUPS
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      ALGEBRAIC CONVERGENCE THEOREMS OF COMPLEX KLEINIAN GROUPS
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1. B. N. Apanasov , Conformal geometry of discrete groups and manifolds (Walter de Gruyter, Berlin, Germany, 2000).

3. W. Cao and X. Wang , Discreteness criteria and algebraic convergence theorem for subgroups in PU(1, n; ℂ), Proc. Japan Acad. 82 (2006), 4952.

5. B. Dai , A. Fang and B. Nai , Discreteness criteria for subgroups in complex hyperbolic space, Proc. Japan Acad. 77 (2001), 168172.

7. T. Jørgensen and P. Klein , Algebraic convergence of finitely generated Kleinian groups, Quart. J. Math. 33 (1982), 325332.

9. G. J. Martin , On discrete Möbius groups in all dimensions, Acta Math. 163 (1989), 253289.

10. J. P. Navarrete , On the limit set of discrete subgroups of PU(2, 1), Geometriae Dedicata 122 (2006), 113.

11. X. Wang , Algebraic convergence theorems of n-dimensional Kleinian groups, Isr. J. Math. 162 (2007), 221233.

12. X. Wang and W. Yang , Discreteness criteria of Möbius groups of high dimensions and convergence theorem of Kleinian groups, Adv. Math. 159 (2001), 6882.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 50 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th September 2017. This data will be updated every 24 hours.