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  1. Of all genus 2 hyperbolic surfaces, the Bolza surface has the highest systole.[1]
  2. The Fuchsian group defining the Bolza surface is also a subgroup of the (3,3,4) triangle group, which is a subgroup of index 2 in the (2,3,8) triangle group.[1]
  3. Of all genus 2 {\displaystyle 2} hyperbolic surfaces, the Bolza surface maximizes the length of the systole (Schmutz 1993).[2]
  4. The Bolza surface is a ( 2 , 3 , 8 ) {\displaystyle (2,3,8)} triangle surface – see Schwarz triangle.[2]
  5. The first eigenspace (that is, the eigenspace corresponding to the first positive eigenvalue) of the Bolza surface is three-dimensional, and the second, four-dimensional (Cook 2018), (Jenni 1981).[2]
  6. In particular, the spectrum of the Bolza surface is known to a very high accuracy (Strohmaier & Uski 2013).[2]
  7. To the best of our knowledge, there is no available software for the simplest possible extension, i.e., the Bolza surface, a hyperbolic manifold homeomorphic to a torus of genus two.[3]
  8. We consider generalized Bolza surfaces Mg, where the octagon is replaced by the regular 4g-gon, leading to a genus g surface.[4]
  9. The Bolza surface is a hyperbolic closed compact orientable surface.[5]
  10. A triangulation of the Bolza surface can be seen as a periodic triangulation of the hyperbolic plane.[5]
  11. The Bolza surface \(\mathcal{M}\) is defined as the quotient of \(\mathbb H^2\) under the action of a group \(\mathcal G\) that we will introduce now.[5]
  12. Figure 44.2 Topological construction of a genus-2 surface from the original domain \(\mathcal D\) of the Bolza surface.[5]
  13. I. Iordanov & M. Teillaud Implementing Delaunay triangulations of the Bolza surface 9 / 33 qXaba(q)ab(q)XbThe Bolza Surface Bolza surface What is it?[6]
  14. (cid:73) Explicit solutions are known on H2 and also on the hyperbolic Bolza surface of genus 2 (Maldonado and NSM).[7]
  15. The algorithm is used to compute the motion of a vortex on the Bolza surface.[8]
  16. The numerical results show that all the 46 vortex equilibria can be explicitly computed using the symmetries of the Bolza surface.[8]
  17. In §4, the algorithm of §2 and the results in §3 are applied to the Bolza surface.[8]
  18. The Bolza surface admits a regular octagonal tiling.[9]
  19. (cid:73) N = 2 Bradlow vortices with separated vortex centres should arise from generic holomorphic 1-forms on the Bolza surface, and the Baptista metric is ||2.[10]
  20. Bolza surface double covers the Riemann sphere.[10]
  21. We give a detailed description of the arithmetic Fuch- sian group of the Bolza surface and the associated quaternion or- der.[11]
  22. However, this congruence subgroup has torsion: it contains an involution closely related to the hyperelliptic involution of the Bolza surface (see Sec- tion 11).[11]
  23. i = SL2(F3), explaining some of the over, we show that symmetries of the Bolza surface.[11]
  24. In particular, we focus on the Bolza surface and the Klein quartic.[12]
  25. Thus, among all CAT(0) metrics, the one with the best systolic ratio is composed of six at regular octagons centered at the Weierstrass points of the Bolza surface.[13]
  26. The inequality is saturated by a singular at metric, with 16 conical singularities, in the conformal class of the Bolza surface.[13]
  27. METRICS IN GENUS TWO 97 The Bolza surface is described in Section 2.[13]
  28. The Bolza surface is also conjectured to be extremal for the rst eigenvalue of the Laplacian.[13]
  29. Distinguishing 16 points on the Bolza surface 3.[14]
  30. (1.1) The inequality is saturated by a singular at metric, with 16 conical singularities, in the conformal class of the Bolza surface.[14]
  31. The Bolza surface is described in Section 2.[14]
  32. The Bolza surface satises SR( ) B Note that Theorems 2.3 and 1.3 imply that SR( B ) 3 .[14]

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