10 papers · 1 filter
The Number of Triangles Needed to Span a Polygon Embedded in R^d
Joel Hass, Jeffrey C. Lagarias
Given a closed polygon P having n edges, embedded in R^d, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface in R^d havin…
The Computational Complexity of Knot Genus and Spanning Area
Ian Agol, Joel Hass, William P. Thurston
We investigate the computational complexity of some problems in three-dimensional topology and geometry. We show that the problem of determining a bound on the genus of a knot in a…
Affine isoperimetric inequalities for piecewise linear surfaces
Joel Hass, Jeffrey C. Lagarias
This paper considers affine analogues of the isoperimetric inequality in the sense of piecewise linear topology. Given a closed polygon P embedded in R^d having n edges, we give up…
On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds
Joel Hass, Shicheng Wang, Qing Zhou
For any hyperbolic 3-manifold with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound…
Boundary slopes of immersed surfaces in 3-manifolds
Joel Hass, J. Hyam Rubinstein, Shicheng Wang
This paper presents some finiteness results for the number of boundary slopes of immersed essential surfaces of given genus g in a compact 3-manifold with torus boundary. In the ca…
The size of spanning disks for polygonal curves
Joel Hass, Jack Snoeyink, William P. Thurston
Let be a closed polygonal curve in $\RR^3$ consisting of line segments. Assume that is unknotted, so that it is the boundary of an embedded disk in $\RR^3$. This paper…