Regular tessellation of the Lobachevskii plane by P.I. Troshin

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The Siegel–Klein Disk: Hilbert Geometry of the Siegel Disk Domain by Frank Nielsen

Subjects: “…hyperbolic geometry…”
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Normalized representation of spin valve resistance value by the hyperbolic metric by Penin Alexandru, Sidorenco Anatoly

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The Principle of Relativity: From Ungar’s Gyrolanguage for Physics to Weaving Computation in Mathematics by Françoise Chatelin

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Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold by Toda Masahito

Subjects: “…hyperbolic geometry…”
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New world from old [kasetvideo]

New worlds from old [filem]

Binary Operations in the Unit Ball: A Differential Geometry Approach by Nikita E. Barabanov, Abraham A. Ungar

“…The binary operation of the Beltrami-Klein ball model of hyperbolic geometry, known as Einstein addition, and the binary operation of the Beltrami-Poincaré ball model of hyperbolic geometry, known as Möbius addition, determine corresponding metric tensors in the unit ball. …”
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Extrapolation over temporal knowledge graph via hyperbolic embedding by Yan Jia, Mengqi Lin, Ye Wang, Jianming Li, Kai Chen, Joanna Siebert, Geordie Z. Zhang, Qing Liao

“…To this end, we propose ReTIN, a novel model integrating real‐time influence of historical facts for TKG reasoning based on hyperbolic geometry, which provides low‐dimensional embeddings to capture latent hierarchical structures and other rich semantic patterns of the existing TKG. …”
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Hyperbolic string tadpole by Atakan Hilmi Firat

“…Hyperbolic geometry on the one-bordered torus is numerically uniformized using Liouville theory. …”
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Lobachevski descubridor de la Geometría Hiperbólica by Juan Boza Cordero

“…1856), which culminated with the discovery of the hyperbolic geometry. We analize the role of the V Postulate in the euclidean geometry and the ways some mathematicians tried to prove it. …”
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Causal structure of the entanglement renormalization ansatz by Cédric Bény

“…It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.…”
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Quantum Hall effect and noncommutative geometry by Carey, A, Hannabuss, K, Mathai, V

“…We study magnetic Schrodinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect (QHE) in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add some refinements to earlier results. …”

UNIFORM SPANNING FORESTS OF PLANAR GRAPHS by TOM HUTCHCROFT, ASAF NACHMIAS

“…We find that the same exponents hold universally over this entire class of graphs provided that measurements are made using the hyperbolic geometry of their circle packings rather than their usual combinatorial geometry.…”
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The Heegaard genus of amalgamated 3-manifolds by Lackenby, M

“…The proof uses the hyperbolic geometry of the amalgamated manifold, generalised Heegaard splittings and minimal surfaces.…”

Skein modules, skein algebra and quantisation by Lee, Benedict Jia Jie

“…The main connection explored here is the quantisation of character variety, which has application in Physics as well as hyperbolic geometry. In this report, we will look at the work by Le, who developed a cutting map which allows one to describe certain classes of skein algebra as well as construct an important map called the quantum trace map. …”
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Continuous hierarchical representations with poincaré Variational Auto-Encoder by Mathieu,E, Le Lan, C, Maddison, CJ, Tomioka, R, Teh, YW

“…We therefore endow VAEs with a Poincaré ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. …”

Elementary knot theory by Lackenby, M

“…In fact, one of the attractions of knot theory is its extensive interactions with many different branches of mathematics: 3-manifold topology, hyperbolic geometry, Teichm¨uller theory, gauge theory, mathematical physics, geometric group theory, graph theory and many other fields.…”

Bootstrapping closed string field theory by Atakan Hilmi Fırat

“…Abstract The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. …”
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COLORING CURVES ON SURFACES by JONAH GASTER, JOSHUA EVAN GREENE, NICHOLAS G. VLAMIS

“…Our investigation leads to connections with Kneser graphs, the Johnson homomorphism, and hyperbolic geometry.…”
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