• Corpus ID: 248496526

Veech Groups and Triangulations of Half-Dilation Pillowcases

@inproceedings{Shima2022VeechGA,
  title={Veech Groups and Triangulations of Half-Dilation Pillowcases},
  author={Taro Shima},
  year={2022}
}
In this paper we consider the symmetries of triangulable half-dilation structures on the sphere with four singularities. We show that all such surfaces can be produced by a tetrahedral construction. Using this construction, we calculate each such surface’s symmetry group in PSL(2 , R ) called the Veech group. 

Figures from this paper

References

SHOWING 1-10 OF 13 REFERENCES

Dilation surfaces and their Veech groups

We introduce a class of objects which we call 'dilation surfaces'. These provide families of foliations on surfaces whose dynamics we are interested in. We present and analyze a couple of examples,

A Discrete Laplace–Beltrami Operator for Simplicial Surfaces

Using Rippa's Theorem, it is shown that, as claimed, Musin’s harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.

Flat Surfaces

Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a

Properties of the Delaunay triangulation

This work defined several functional on the set of all triangulations of the finite system of sites in Rd attaining global minimum on the Delaunay triangulation (DT), and considers a so called “parabolic” functional and proves that it attains its minimum on DT in all dimensions.

American Journal of Mathematics

  • Mathematics
    Nature
  • 1886
WE are glad to note that the successive parts now appear with praiseworthy regularity, and the arrival of our number can be predicted to a very close order of approximation. The volume opens with a

TH'

The present study examined how dopamine neurons in the ventral tegmental area respond to aversive events in various conditions and showed that mate-guarding affects female mate choice, and identified a novel IEG encoding a Ser/Thr protein kinase (provisionally named as #15 ).

Topology

Discrete Comput

  • Geom., (38):740– 756,
  • 2007