# 볼차 곡면

## 노트

### 말뭉치

- Of all genus 2 hyperbolic surfaces, the Bolza surface has the highest systole.
^{[1]} - 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]} - Of all genus 2 {\displaystyle 2} hyperbolic surfaces, the Bolza surface maximizes the length of the systole (Schmutz 1993).
^{[2]} - The Bolza surface is a ( 2 , 3 , 8 ) {\displaystyle (2,3,8)} triangle surface – see Schwarz triangle.
^{[2]} - 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]} - In particular, the spectrum of the Bolza surface is known to a very high accuracy (Strohmaier & Uski 2013).
^{[2]} - 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]} - We consider generalized Bolza surfaces Mg, where the octagon is replaced by the regular 4g-gon, leading to a genus g surface.
^{[4]} - The Bolza surface is a hyperbolic closed compact orientable surface.
^{[5]} - A triangulation of the Bolza surface can be seen as a periodic triangulation of the hyperbolic plane.
^{[5]} - 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]} - Figure 44.2 Topological construction of a genus-2 surface from the original domain \(\mathcal D\) of the Bolza surface.
^{[5]} - 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]} - (cid:73) Explicit solutions are known on H2 and also on the hyperbolic Bolza surface of genus 2 (Maldonado and NSM).
^{[7]} - The algorithm is used to compute the motion of a vortex on the Bolza surface.
^{[8]} - The numerical results show that all the 46 vortex equilibria can be explicitly computed using the symmetries of the Bolza surface.
^{[8]} - In §4, the algorithm of §2 and the results in §3 are applied to the Bolza surface.
^{[8]} - The Bolza surface admits a regular octagonal tiling.
^{[9]} - (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]} - Bolza surface double covers the Riemann sphere.
^{[10]} - We give a detailed description of the arithmetic Fuch- sian group of the Bolza surface and the associated quaternion or- der.
^{[11]} - 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]} - i = SL2(F3), explaining some of the over, we show that symmetries of the Bolza surface.
^{[11]} - In particular, we focus on the Bolza surface and the Klein quartic.
^{[12]} - 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]} - The inequality is saturated by a singular at metric, with 16 conical singularities, in the conformal class of the Bolza surface.
^{[13]} - METRICS IN GENUS TWO 97 The Bolza surface is described in Section 2.
^{[13]} - The Bolza surface is also conjectured to be extremal for the rst eigenvalue of the Laplacian.
^{[13]} - Distinguishing 16 points on the Bolza surface 3.
^{[14]} - (1.1) The inequality is saturated by a singular at metric, with 16 conical singularities, in the conformal class of the Bolza surface.
^{[14]} - The Bolza surface is described in Section 2.
^{[14]} - The Bolza surface satises SR( ) B Note that Theorems 2.3 and 1.3 imply that SR( B ) 3 .
^{[14]}

### 소스

- ↑
^{1.0}^{1.1}Bolza surface - ↑
^{2.0}^{2.1}^{2.2}^{2.3}Bolza surface - ↑ Implementing Delaunay Triangulations of the Bolza Surface
- ↑ Delaunay triangulations of generalized Bolza surfaces
- ↑
^{5.0}^{5.1}^{5.2}^{5.3}2D Periodic Hyperbolic Triangulations: User Manual - ↑ Implementing delaunay triangulations
- ↑ Exotic vortices and their dynamics
- ↑
^{8.0}^{8.1}^{8.2}The motion of a vortex on a closed surface of constant negative curvature - ↑ Clebsch Graph Surface Tiling and the Hurwitz Automorphism Theorem
- ↑
^{10.0}^{10.1}Vortices and cones - ↑
^{11.0}^{11.1}^{11.2}Bolza quaternion order and asymptotics - ↑ Properties of eigenvalues on Riemann surfaces with large symmetry groups
- ↑
^{13.0}^{13.1}^{13.2}^{13.3}Paciﬁc - ↑
^{14.0}^{14.1}^{14.2}^{14.3}An optimal systolic inequality for cat(0)