Research
A
quasifuchsian group
My main areas of research are Hyperbolic geometry, and Kleinian groups.
Current research includes studying the relation
between the geometry of the convex hull of a Kleinian group and the
Hausdorf dimension of the limit set via length
distortion of the Patterson-Sullivan measure of the Kleinian group.
1. The structure and enumeration of link projections
Transactions
of the American Mathematical Society, Volume 348, No.
6, June 1996
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2. Bounds on volume increase under dehn drilling operations
Proceedings
of the
London Mathematical Society
, Volume 77, No. 3, 1998
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3. Average curvature of convex curves in H2
Proceedings
of the
American Mathematical Society
, Volume 126, No. 1, January 1998
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4. Average bending of convex pleated planes in H3
inventiones
mathematicae, Volume 132,
1998
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5. Length distortion and the hausdorff dimension of limit sets
co-author:
Edward Taylor
American Journal of Mathematics,
Volume 122, 2000
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6. From the boundary of the convex core to the conformal boundary
co-author: Richard Canary
Geometrica Dedicata,
Volume 96, No. 1, 2003
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7. Bounds on the average bending of the convex hull of a Kleinian group
Michigan Math Journal,
Volume 51, No. 2, 2003
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8. Random geodesics
In the tradition of Ahlfors and
Bers, III.
AMS Contemporary Math Series, Volume 355, 2004
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9.
Distortion of the exponent of convergence in space
co-authors: Petra Bonfert-Taylor and
Edward C. Taylor
Annales Academicae Scientiarum
Fennicae
Mathematica, Volume 29, 2004
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10. Bounding the bending of a hyperbolic three-manifold
co-author:
Richard Canary
Pacific Journal of Math, Volume 218, No. 2, 2005
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11. Patterson-Sullivan measures and quasi-conformal deformations
co-author:
Edward Taylor
Communications in
Analysis and Geometry, Volume 13, No. 3, 2005
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12. Distribution of intersection lengths of a random geodesic
with a geodesic lamination
co-author: David Dumas
Ergodic Theory and
Dynamical Systems, Volume 27, No. 4, 2007
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13. Quasiconformal homogeneity of hyperbolic surfaces with fixed-point full automorphisms
co-authors:
Petra Bonfert-Taylor, Richard Canary, and Edward Taylor
Proceedings of the Cambridge Philosophical Society, Volume 143, Issue 01,
July 2007
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14. An extension of the Weil-Petersson metric to quasi-fuchsian
space.
co-author:
Edward Taylor
Mathematische Annalen, Volume
341, Number 4, August, 2008
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15. Critical points of Hausdorff dimension and the Weil-Petersson extension to quasifuchsian space
To appear Geometry and
Topology, 2010
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16. Orthospectra of Geodesic Laminations and Dilogarithm Identities on Moduli Space
Preprint, January 2009
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17. Hyperbolic volume of n-manifolds with geodesic boundary and orthospectra
co-author: Jeremy Kahn
Preprint, July 2009
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18. The Thurston Metric on Hyperbolic Domains and Boundaries of Convex Hulls
co-author: Richard Canary
Preprint, February 2010
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