Zobrazeno 1 - 10
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pro vyhledávání: '"Mcshane, Greg"'
Autor:
McShane, Greg
We discuss the relationship between Penner's $\lambda$-length and the norms of Eisenstein integers. This leads to a geometric proof of the fact, attributed to Fermat, that every prime $p$ of the form $3k + 1$ is the norm of an Eisenstein integer that
Externí odkaz:
http://arxiv.org/abs/2403.14375
Autor:
Masai, Hidetoshi, McShane, Greg
A number of questions related to the length spectrum of surfaces are discussed and in particular the existence of pairs of surfaces which though not isometric are isospectral. Here by isospectral we mean that a pair of bodies have the same distributi
Externí odkaz:
http://arxiv.org/abs/2308.12109
Autor:
McShane, Greg
Markov numbers are integers that appear in triples which are solutions of a Diophantine equation, the so-called Markov cubic $$x^2 + y^2 + z^2 - 3x y z = 0.$$ A classical topic in number theory, these numbers are related to many areas of mathematics
Externí odkaz:
http://arxiv.org/abs/2101.03316
Autor:
McShane, Greg
Counting integer points on the Markoff cubic is closely related to questions in hyperbolic geometry. In a previous work with Igor Rivin we investigated the regularity of the geodesic length function for a punctured torus. Here we extend this work to
Externí odkaz:
http://arxiv.org/abs/2003.05967
Autor:
Masai, Hidetoshi, McShane, Greg
We consider the ortho spectrum of hyperbolic surfaces with totally geodesic boundary. We show that in general the ortho spectrum does not determine the systolic length but that there are only finitely many possibilities. As a corollary we show that,
Externí odkaz:
http://arxiv.org/abs/1909.09829
Autor:
McShane, Greg
The set of axes of hyperbolic elements in a Fuchsian group depends on the commensurability class of the group. In fact, it has been conjectured that it determines the commensurability class and this has been verified in for groups of the second kind
Externí odkaz:
http://arxiv.org/abs/1709.08958
The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane
Externí odkaz:
http://arxiv.org/abs/1509.03790
Autor:
McShane, Greg
Do and Norbury found a so-called differential relation which relates the volume of the moduli space of singular surface with a cone point to that of a smooth surface obtained by forgetting the cone point. Their procedure is valid for cone angles less
Externí odkaz:
http://arxiv.org/abs/1503.00539
Autor:
Kojima, Sadayoshi, McShane, Greg
Publikováno v:
Geom. Topol. 22 (2018) 2403-2426
Thanks to a recent result by Jean-Marc Schlenker, we establish an explicit linear inequality between the normalized entropies of pseudo-Anosov automorphisms and the hyperbolic volumes of their mapping tori. As its corollaries, we give an improved low
Externí odkaz:
http://arxiv.org/abs/1411.6350
Autor:
Penner, R. C., McShane, Greg
The mapping class group invariant ideal cell decomposition of the Teichmueller space of a punctured surface times an open simplex has been used in a number of computations. This paper answers a question about the asymptotics of this decomposition, na
Externí odkaz:
http://arxiv.org/abs/0707.1468