3,928 research outputs found
A characterization of short curves of a Teichmueller geodesic
We provide a combinatorial condition characterizing curves that are short
along a Teichmueller geodesic. This condition is closely related to the
condition provided by Minsky for curves in a hyperbolic 3-manifold to be short.
We show that short curves in a hyperbolic manifold homeomorphic to S x R are
also short in the corresponding Teichmueller geodesic, and we provide examples
demonstrating that the converse is not true.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper5.abs.htm
On spun-normal and twisted squares surfaces
Given a 3 manifold M with torus boundary and an ideal triangulation, Yoshida
and Tillmann give different methods to construct surfaces embedded in M from
ideal points of the deformation variety. Yoshida builds a surface from twisted
squares whereas Tillmann produces a spun-normal surface. We investigate the
relation between the generated surfaces and extend a result of Tillmann's (that
if the ideal point of the deformation variety corresponds to an ideal point of
the character variety then the generated spun-normal surface is detected by the
character variety) to the generated twisted squares surfaces.Comment: 14 pages, 10 figure
Wrapping an adhesive sphere with a sheet
We study the adhesion of an elastic sheet on a rigid spherical substrate.
Gauss'Theorema Egregium shows that this operation necessarily generates metric
distortions (i.e. stretching) as well as bending. As a result, a large variety
of contact patterns ranging from simple disks to complex branched shapes are
observed as a function of both geometrical and material properties. We describe
these different morphologies as a function of two non-dimensional parameters
comparing respectively bending and stretching energies to adhesion. A complete
configuration diagram is finally proposed
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