Equilateral Convex Triangulations of ℝ P 2 $$\mathbb R P^2$$ with Three Conical Points of Equal Defect

Mikhail Chernavskikh (), Altan Erdnigor (), Nikita Kalinin () and Alexandr Zakharov ()
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Mikhail Chernavskikh: Lomonosov Moscow State University
Altan Erdnigor: HSE University, Russian Federation, Department of Mathematics
Nikita Kalinin: Saint Petersburg State University
Alexandr Zakharov: Saint Petersburg State University

Chapter Chapter 9 in In the Tradition of Thurston II, 2022, pp 315-329 from Springer

Abstract: Abstract Consider triangulations of ℝ P 2 $$\mathbb R P^2$$ whose all vertices have valency six except three vertices of valency 4. In this chapter we prove that the number f(n) of such triangulations with no more than n triangles grows as C ⋅ n2 + O(n3∕2) where , where is the Lobachevsky function and ζ ( Eis , 2 ) = ∑ ( a , b ) ∈ ℤ 2 ∖ 0 1 | a + b ω 2 | 4 $$\zeta (\mathit {Eis},2) =\sum \limits _{(a,b)\in \mathbb Z^2\setminus 0}{\frac {1}{|a+b\omega ^2|{ }^4}}$$ , and ω6 = 1.

Keywords: Flat metric; Equilateral triangulation; Conical singularity; Zeta function; Epstein zeta function; Hyperbolic volume; 51M09; 57N45; 11P21; 11M36; 11E45 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-97560-9_9

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DOI: 10.1007/978-3-030-97560-9_9

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