Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Limit Sets of Discrete Groups of Isometries of Exotic Hyperbolic Spaces

Kevin Corlette and Alessandra Iozzi
Transactions of the American Mathematical Society
Vol. 351, No. 4 (Apr., 1999), pp. 1507-1530
Stable URL: http://www.jstor.org/stable/117857
Page Count: 24
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Limit Sets of Discrete Groups of Isometries of Exotic Hyperbolic Spaces
Preview not available

Abstract

Let Γ be a geometrically finite discrete group of isometries of hyperbolic space HF n, where F = R, C, H or O (in which case n = 2). We prove that the critical exponent of Γ equals the Hausdorff dimension of the limit sets Λ (Γ) and that the smallest eigenvalue of the Laplacian acting on square integrable functions is a quadratic function of either of them (when they are sufficiently large). A generalization of Hopf ergodicity theorem for the geodesic flow with respect to the Bowen-Margulis measure is also proven.

Page Thumbnails

  • Thumbnail: Page 
1507
    1507
  • Thumbnail: Page 
1508
    1508
  • Thumbnail: Page 
1509
    1509
  • Thumbnail: Page 
1510
    1510
  • Thumbnail: Page 
1511
    1511
  • Thumbnail: Page 
1512
    1512
  • Thumbnail: Page 
1513
    1513
  • Thumbnail: Page 
1514
    1514
  • Thumbnail: Page 
1515
    1515
  • Thumbnail: Page 
1516
    1516
  • Thumbnail: Page 
1517
    1517
  • Thumbnail: Page 
1518
    1518
  • Thumbnail: Page 
1519
    1519
  • Thumbnail: Page 
1520
    1520
  • Thumbnail: Page 
1521
    1521
  • Thumbnail: Page 
1522
    1522
  • Thumbnail: Page 
1523
    1523
  • Thumbnail: Page 
1524
    1524
  • Thumbnail: Page 
1525
    1525
  • Thumbnail: Page 
1526
    1526
  • Thumbnail: Page 
1527
    1527
  • Thumbnail: Page 
1528
    1528
  • Thumbnail: Page 
1529
    1529
  • Thumbnail: Page 
1530
    1530