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Journal articles on the topic 'Hyperbolic space'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Porechnaia, Viktoriia I. "Convergence of metaphorization and hyperbolization (semantic space expansion): Tropeic and cognitive aspects." Current Issues in Philology and Pedagogical Linguistics, no. 4 (December 25, 2024): 187–97. https://doi.org/10.29025/2079-6021-2024-4-187-197.

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The aim of this article is to study the metaphorization and hyperbolization processes in a comparative aspect. The material of the study is 14 contexts of the use of metaphors, hyperbolic and hyperbolic metaphors, one of the verbalization elements of which is a lexeme with the spatial meaning “sea”. The study of these tropes with a spatial component is due to the importance of this category in the worldview in general and the linguistic worldview in particular. The material source is the Russian National Corpus. In the course of the research, methods of description, comparison, generalization,

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2

Zenginoğlu, Anıl. "Hyperbolic times in Minkowski space." American Journal of Physics 92, no. 12 (2024): 965–74. http://dx.doi.org/10.1119/5.0214271.

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Time functions with asymptotically hyperbolic geometry play an increasingly important role in many areas of relativity, from computing black hole perturbations to analyzing wave equations. Despite their significance, many of their properties remain underexplored. In this expository article, I discuss hyperbolic time functions by considering the hyperbola as the relativistic analog of a circle in two-dimensional Minkowski space and argue that suitably defined hyperboloidal coordinates are as natural in Lorentzian manifolds as spherical coordinates are in Riemannian manifolds.

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3

Levitt, Gilbert, and Harold Rosenberg. "hyperbolic space." Duke Mathematical Journal 52, no. 1 (1985): 53–59. http://dx.doi.org/10.1215/s0012-7094-85-05204-4.

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4

Babich, M., and A. Bobenko. "hyperbolic space." Duke Mathematical Journal 72, no. 1 (1993): 151–85. http://dx.doi.org/10.1215/s0012-7094-93-07207-9.

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5

IZUMIYA, SHYUICHI, DONGHE PEI, and TAKASI SANO. "SINGULARITIES OF HYPERBOLIC GAUSS MAPS." Proceedings of the London Mathematical Society 86, no. 2 (2003): 485–512. http://dx.doi.org/10.1112/s0024611502013850.

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In this paper we adopt the hyperboloid in Minkowski space as the model of hyperbolic space. We define the hyperbolic Gauss map and the hyperbolic Gauss indicatrix of a hypersurface in hyperbolic space. The hyperbolic Gauss map has been introduced by Ch. Epstein [J. Reine Angew. Math. 372 (1986) 96–135] in the Poincaré ball model, which is very useful for the study of constant mean curvature surfaces. However, it is very hard to perform the calculation because it has an intrinsic form. Here, we give an extrinsic definition and we study the singularities. In the study of the singularities of the

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6

Dursun, Uğur, and Rüya Yeğin. "Hyperbolic submanifolds with finite type hyperbolic Gauss map." International Journal of Mathematics 26, no. 02 (2015): 1550014. http://dx.doi.org/10.1142/s0129167x15500147.

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We study submanifolds of hyperbolic spaces with finite type hyperbolic Gauss map. First, we classify the hyperbolic submanifolds with 1-type hyperbolic Gauss map. Then we prove that a non-totally umbilical hypersurface Mn with nonzero constant mean curvature in a hyperbolic space [Formula: see text] has 2-type hyperbolic Gauss map if and only if M has constant scalar curvature. We also classify surfaces with constant mean curvature in the hyperbolic space [Formula: see text] having 2-type hyperbolic Gauss map. Moreover we show that a horohypersphere in [Formula: see text] has biharmonic hyperb

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7

Chen, Chiang-Mei, Pei-Ming Ho, Ishwaree P. Neupane, John E. Wang, and Nobuyoshi Ohta. "Hyperbolic space cosmologies." Journal of High Energy Physics 2003, no. 10 (2003): 058. http://dx.doi.org/10.1088/1126-6708/2003/10/058.

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8

Xuegang, Yu. "Hyperbolic Hilbert space." Advances in Applied Clifford Algebras 10, no. 1 (2000): 49–60. http://dx.doi.org/10.1007/bf03042009.

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9

Wijana, I. Dewa Putu. "Hyperbole in Indonesian Song Lyrics." Journal of Language and Literature 25, no. 1 (2025): 240–49. https://doi.org/10.24071/joll.v25i1.10316.

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Language is pivotal in fulfilling human communicative needs, such as transactional and interactional functions. In the latter function, language is employed, one of which is to build social and personal attitudes, or so-called poetic or imaginative function. Such functions can be accessed through songs or song lyrics. Motivated by the previous argument, this paper aims to describe construction types and categories of hyperbolic expressions found in various Indonesian song lyrics, comprising the genres of “kroncong,” “dangdut,” and other popular songs. To provide the evidence, this study collec

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10

Yegin, R., and U. Dursun. "On Submanifolds of Pseudo-Hyperbolic Space with 1-Type Pseudo-Hyperbolic Gauss Map." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 4 (2016): 315–37. http://dx.doi.org/10.15407/mag12.04.315.

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11

THAI, DO DUC, and PHAM VIET DUC. "THE KOBAYASHI k-METRICS ON COMPLEX SPACES." International Journal of Mathematics 10, no. 07 (1999): 917–24. http://dx.doi.org/10.1142/s0129167x99000392.

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In this article we are going to give a characterization of the hyperbolicity of complex spaces through the Kobayashi k-metrics on complex spaces and to give an integrated representation of the Kobayashi pseudo-distance on any complex space. Moreover, it is shown that a complex space is hyperbolic iff every irreducible branch of this space is hyperbolic.

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12

Abbott, Carolyn, Jason Behrstock, and Matthew Durham. "Largest acylindrical actions and Stability in hierarchically hyperbolic groups." Transactions of the American Mathematical Society, Series B 8, no. 3 (2021): 66–104. http://dx.doi.org/10.1090/btran/50.

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We consider two manifestations of non-positive curvature: acylindrical actions (on hyperbolic spaces) and quasigeodesic stability. We study these properties for the class of hierarchically hyperbolic groups, which is a general framework for simultaneously studying many important families of groups, including mapping class groups, right-angled Coxeter groups, most 3 3 –manifold groups, right-angled Artin groups, and many others. A group that admits an acylindrical action on a hyperbolic space may admit many such actions on different hyperbolic spaces. It is natural to try to develop an understa

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13

Lam, Ho-Ching, and Ivo D. Dinov. "Hyperbolic Wheel: A Novel Hyperbolic Space Graph Viewer for Hierarchical Information Content." ISRN Computer Graphics 2012 (October 31, 2012): 1–10. http://dx.doi.org/10.5402/2012/609234.

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Tree and graph structures have been widely used to present hierarchical and linked data. Hyperbolic trees are special types of graphs composed of nodes (points or vertices) and edges (connecting lines), which are visualized on a non-Euclidean space. In traditional Euclidean space graph visualization, distances between nodes are measured by straight lines. Displays of large graphs in Euclidean spaces may not utilize efficiently the available space and may impose limitations on the number of graph nodes. The special hyperbolic space rendering of tree-graphs enables adaptive and efficient use of

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14

Tang, Shuan, та Pengcheng Wu. "Composition Operator, Boundedness, Compactness, Hyperbolic Bloch-Type Space βμ∗, Hyperbolic-Type Space". Journal of Function Spaces 2020 (1 серпня 2020): 1–7. http://dx.doi.org/10.1155/2020/5390732.

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In this paper, we obtain some characterizations of composition operators Cφ, which are induced by an analytic self-map φ of the unit disk Δ, from hyperbolic Bloch type space βμ∗ into hyperbolic type space QK,p,q∗.

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15

Mak, Mahmut, and Baki Karlığa. "Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/838564.

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We consider hyperbolic rotation (G0), hyperbolic translation (G1), and horocyclic rotation (G2) groups inH3, which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups ofG0inH3. Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator inH3.

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16

Blåsjö, Viktor. "Hyperbolic Space for Tourists." Journal of Humanistic Mathematics 3, no. 2 (2013): 77–95. http://dx.doi.org/10.5642/jhummath.201302.06.

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17

Chaturvedi, S., G. J. Milburn, and Zhongxi Zhang. "Interference in hyperbolic space." Physical Review A 57, no. 3 (1998): 1529–35. http://dx.doi.org/10.1103/physreva.57.1529.

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18

Bezdek, Károly, Márton Naszódi, and Deborah Oliveros. "Antipodality in hyperbolic space." Journal of Geometry 85, no. 1-2 (2006): 22–31. http://dx.doi.org/10.1007/s00022-006-0038-0.

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19

Kaliman, Shulim, and Mikhail Zaidenberg. "Non-hyperbolic complex space with a hyperbolic normalization." Proceedings of the American Mathematical Society 129, no. 5 (2000): 1391–93. http://dx.doi.org/10.1090/s0002-9939-00-05711-7.

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20

Yakut, Atakan Tuğkan, Murat Savaş, and Tuğba Tamirci. "The Smarandache Curves onS12and Its Duality onH02." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/193586.

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We introduce special Smarandache curves based on Sabban frame onS12and we investigate geodesic curvatures of Smarandache curves on de Sitter and hyperbolic spaces. The existence of duality between Smarandache curves on de Sitter space and Smarandache curves on hyperbolic space is shown. Furthermore, we give examples of our main results.

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21

Zhou, Anjie, Kaixin Yao, and Donghe Pei. "k-type hyperbolic framed slant helices in hyperbolic 3-space." Filomat 38, no. 11 (2024): 3839–50. https://doi.org/10.2298/fil2411839z.

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In this paper, we give the existence and uniqueness theorems for hyperbolic framed curves and define the k-type hyperbolic framed slant helices in three-dimensional hyperbolic space. Using the hyperbolic curvature, we investigate the k-type hyperbolic framed slant helices and the connection between them. Hyperbolic framed slant helices might have singular points, they are a generalization of hyperbolic slant helices. Moreover, as their applications, we give some examples of k-type hyperbolic framed slant helices.

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22

PARKER, JOHN R. "SHIMIZU’S LEMMA FOR COMPLEX HYPERBOLIC SPACE." International Journal of Mathematics 03, no. 02 (1992): 291–308. http://dx.doi.org/10.1142/s0129167x92000096.

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Shimizu’s lemma gives a necessary condition for a discrete group of isometries of the hyperbolic plane containing a parabolic map to be discrete. Viewing the hyperbolic plane as complex hyperbolic 1-space we generalise Shimizu’s lemma to higher dimensional complex hyperbolic space In particular we give a version of Shimizu’s lemma for subgroups of PU (n, 1) containing a vertical translation Partial generalisation to groups containing either an ellipto-parabolic map or non-vertical translations are also given together with examples that show full generalisation is not possible in these cases

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23

Rogovin, Sari, Hyogo Shibahara, and Qingshan Zhou. "Some remarks on the Gehring–Hayman theorem." Annales Fennici Mathematici 48, no. 1 (2023): 141–52. http://dx.doi.org/10.54330/afm.125920.

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In this paper we provide new characterizations of the Gehring–Hayman theorem from the point of view of Gromov boundary and uniformity. We also determine the critical exponents for the uniformized space to be a uniform space in the case of the hyperbolic spaces, the model spaces \(\mathbb{M}^{\kappa}_n\) of the sectional curvature \(\kappa<0\) with the dimension \(n \geq 2\) and hyperbolic fillings.

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24

Khalfallah, Adel. "The moduli space of hyperbolic compact complex spaces." Mathematische Zeitschrift 255, no. 4 (2006): 691–702. http://dx.doi.org/10.1007/s00209-006-0036-9.

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25

Jenkovszky, L. L., Y. A. Kurochkin, V. S. Otchik, P. F. Pista, N. D. Shaikovskaya, and D. V. Shoukavy. "Theory of Quantum Mechanical Scattering in Hyperbolic Space." Symmetry 15, no. 2 (2023): 377. http://dx.doi.org/10.3390/sym15020377.

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The theory of quantum mechanical scattering in hyperbolic space is developed. General formulas based on usage of asymptotic form of the solution of the Shrödinger equation in hyperbolic space are derived. The concept of scattering length in hyperbolic space, a convenient measurable in describing low-energy nuclear interactions is introduced. It is shown that, in the limit of the flat space, i.e., when ρ→∞, the obtained expressions for quantum mechanical scattering in hyperbolic space transform to corresponding formulas in three-dimensional Euclidean space.

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26

Stroethoff, Karel. "Besov-type characterisations for the Bloch space." Bulletin of the Australian Mathematical Society 39, no. 3 (1989): 405–20. http://dx.doi.org/10.1017/s0004972700003324.

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We will prove local and global Besov-type characterisations for the Bloch space and the little Bloch space. As a special case we obtain that the Bloch space consists of those analytic functions on the unit disc whose restrictions to pseudo-hyperbolic discs (of fixed pseudo-hyperbolic radius) uniformly belong to the Besov space. We also generalise the results to Bloch functions and little Bloch functions on the unit ball in . Finally we discuss the related spaces BMOA and VMOA.

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27

KAPOVICH, ILYA, and MARTIN LUSTIG. "PING-PONG AND OUTER SPACE." Journal of Topology and Analysis 02, no. 02 (2010): 173–201. http://dx.doi.org/10.1142/s1793525310000318.

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We prove that, if φ, ψ ∈ Out (FN) are hyperbolic iwips (irreducible with irreducible powers) such that 〈φ, ψ〉 ⊆ Out (FN) is not virtually cyclic, then some high powers of φ and ψ generate a free subgroup of rank two for which all nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of Out (FN) is strongly analogous to being a pseudo-Anosov element of a mapping class group, so the above result provides analogues of "purely pseudo-Anosov" free subgroups in Out (FN).

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28

Hyde, Stephen T., Ann-Kristin Larsson, Tiziana Di Matteo, Stuart Ramsden, and Vanessa Robins. "Meditation on an Engraving of Fricke and Klein (The Modular Group and Geometrical Chemistry)." Australian Journal of Chemistry 56, no. 10 (2003): 981. http://dx.doi.org/10.1071/ch03191.

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A non-technical account of the links between two-dimensional (2D) hyperbolic and three-dimensional (3D) euclidean symmetric patterns is presented, with a number of examples from both spaces. A simple working hypothesis is used throughout the survey: simple, highly symmetric patterns traced in hyperbolic space lead to chemically relevant structures in euclidean space. The prime examples in the former space are derived from Felix Klein's engraving of the modular group structure within the hyperbolic plane; these include various tilings, networks and trees. Disc packings are also derived. The euc

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29

TRAN, HUNG CONG. "RELATIONS BETWEEN VARIOUS BOUNDARIES OF RELATIVELY HYPERBOLIC GROUPS." International Journal of Algebra and Computation 23, no. 07 (2013): 1551–72. http://dx.doi.org/10.1142/s0218196713500367.

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Suppose a group G is relatively hyperbolic with respect to a collection ℙ of its subgroups and also acts properly, cocompactly on a CAT(0) (or δ-hyperbolic) space X. The relatively hyperbolic structure provides a relative boundary ∂(G, ℙ). The CAT(0) structure provides a different boundary at infinity ∂X. In this paper, we examine the connection between these two spaces at infinity. In particular, we show that ∂(G, ℙ) is G-equivariantly homeomorphic to the space obtained from ∂X by identifying the peripheral limit points of the same type.

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30

CASTRO, C., and J. A. NIETO. "ON (2+2)-DIMENSIONAL SPACE–TIMES, STRINGS AND BLACK HOLES." International Journal of Modern Physics A 22, no. 11 (2007): 2021–45. http://dx.doi.org/10.1142/s0217751x07036191.

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We study black hole-like solutions (space–times with singularities) of Einstein field equations in 3+1 and 2+2 dimensions. We find three different cases associated with hyperbolic homogeneous spaces. In particular, the hyperbolic version of Schwarzschild's solution contains a conical singularity at r = 0 resulting from pinching to zero size r = 0 the throat of the hyperboloid [Formula: see text] and which is quite different from the static spherically symmetric (3+1)-dimensional solution. Static circular symmetric solutions for metrics in 2+2 are found that are singular at ρ = 0 and whose asym

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31

Al Ghafri, Mohammed Said, Yousef Estaremi, and Zhidong Huang. "Orlicz Spaces and Their Hyperbolic Composition Operators." Mathematics 12, no. 18 (2024): 2809. http://dx.doi.org/10.3390/math12182809.

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In this paper, by extending some Lp-norm inequalities to similar inequalities for Orlicz space (LΦ-norm), we provide equivalent conditions for composition operators to have the shadowing property on the Orlicz space LΦ(μ). Additionally, we show that for composition operators on Orlicz spaces, the concepts of generalized hyperbolicity and the shadowing property are equivalent. These results extend similar findings on Lp-spaces to Orlicz spaces.

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32

Gaillard, Pierre-Yves. "Harmonic Spinors on Hyperbolic Space." Canadian Mathematical Bulletin 36, no. 3 (1993): 257–62. http://dx.doi.org/10.4153/cmb-1993-037-7.

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AbstractThe purpose for this short note is to describe the space of harmonic spinors on hyperbolicn-spaceHn. This is a natural continuation of the study of harmonic functions onHnin [Minemura] and [Helgason]—these results were generalized in the form of Helgason's conjecture, proved in [KKMOOT],—and of [Gaillard 1, 2], where harmonic forms onHnwere considered. The connection between invariant differential equations on a Riemannian semisimple symmetric spaceG/Kand homological aspects of the representation theory ofG, as exemplified in (8) below, does not seem to have been previously mentioned.

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33

Pavlov, D. G., and S. S. Kokarev. "Hyperbolic statics in space-time." Gravitation and Cosmology 21, no. 2 (2015): 152–56. http://dx.doi.org/10.1134/s0202289315020097.

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34

Bestvina, Mladen. "Degenerations of the hyperbolic space." Duke Mathematical Journal 56, no. 1 (1988): 143–61. http://dx.doi.org/10.1215/s0012-7094-88-05607-4.

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35

Söderberg, B. "Bethe lattices in hyperbolic space." Physical Review E 47, no. 6 (1993): 4582–84. http://dx.doi.org/10.1103/physreve.47.4582.

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36

Benjamini, Itai, and Yury Makarychev. "Dimension reduction for hyperbolic space." Proceedings of the American Mathematical Society 137, no. 02 (2008): 695–98. http://dx.doi.org/10.1090/s0002-9939-08-09714-1.

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37

Chen, Chiang-Mei, Pei-Ming Ho, Ishwaree P. Neupane, Nobuyoshi Ohta, and John E. Wang. "Addendum to ``Hyperbolic space cosmologies''." Journal of High Energy Physics 2006, no. 11 (2006): 044. http://dx.doi.org/10.1088/1126-6708/2006/11/044.

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38

Lück, Reinhard. "Quasiperiodic tilings in hyperbolic space." Journal of Physics: Conference Series 1458 (January 2020): 012009. http://dx.doi.org/10.1088/1742-6596/1458/1/012009.

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39

Kellerhals, R. "Volumes in hyperbolic 5-space." Geometric and Functional Analysis 5, no. 4 (1995): 640–67. http://dx.doi.org/10.1007/bf01902056.

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40

Barbot, Thierry. "Globally hyperbolic flat space–times." Journal of Geometry and Physics 53, no. 2 (2005): 123–65. http://dx.doi.org/10.1016/j.geomphys.2004.05.002.

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41

Coskunuzer, Baris. "Minimal Planes in Hyperbolic Space." Communications in Analysis and Geometry 12, no. 4 (2004): 821–36. http://dx.doi.org/10.4310/cag.2004.v12.n4.a3.

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42

Popov, Maxim. "Instantons on hyperbolic four-space." Modern Physics Letters A 30, no. 28 (2015): 1550140. http://dx.doi.org/10.1142/s0217732315501400.

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43

Dajczer, M., and Th Vlachos. "Kaehler submanifolds of hyperbolic space." Proceedings of the American Mathematical Society 148, no. 9 (2020): 4015–24. http://dx.doi.org/10.1090/proc/15007.

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44

Palmer, Bennett. "Surfaces in Lorentzian hyperbolic space." Annals of Global Analysis and Geometry 9, no. 2 (1991): 117–28. http://dx.doi.org/10.1007/bf00776851.

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45

Balogh, Zoltán M., and Annina Iseli. "Projection theorems in hyperbolic space." Archiv der Mathematik 112, no. 3 (2018): 329–36. http://dx.doi.org/10.1007/s00013-018-1252-3.

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46

Cao, Zongsheng, Qianqian Xu, Zhiyong Yang, Xiaochun Cao, and Qingming Huang. "Geometry Interaction Knowledge Graph Embeddings." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (2022): 5521–29. http://dx.doi.org/10.1609/aaai.v36i5.20491.

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Knowledge graph (KG) embeddings have shown great power in learning representations of entities and relations for link prediction tasks. Previous work usually embeds KGs into a single geometric space such as Euclidean space (zero curved), hyperbolic space (negatively curved) or hyperspherical space (positively curved) to maintain their specific geometric structures (e.g., chain, hierarchy and ring structures). However, the topological structure of KGs appears to be complicated, since it may contain multiple types of geometric structures simultaneously. Therefore, embedding KGs in a single space

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47

Jamadandi, Adarsh, and Uma Mudenagudi. "Dethroning Aristocracy in Graphs via Adversarial Perturbations (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 18 (2021): 15801–2. http://dx.doi.org/10.1609/aaai.v35i18.17897.

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Learning low-dimensional embeddings of graph data in curved Riemannian manifolds has gained traction due to their desirable property of acting as effective geometrical inductive biases. More specifically, models of Hyperbolic geometry such as Poincar\'{e} Ball and Lorentz/Hyperboloid Model have found applications for learning data with hierarchical anatomy. Gromov's hyperbolicity measures whether a graph can be isometrically embedded in hyperbolic space. This paper shows that adversarial attacks that perturb the network structure also affect the hyperbolicity of graphs rendering hyperbolic spa

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48

Zhang, Xiaoming, Dongjie Tian, and Huiyong Wang. "Knowledge Graph Completion Based on Entity Descriptions in Hyperbolic Space." Applied Sciences 13, no. 1 (2022): 253. http://dx.doi.org/10.3390/app13010253.

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Hyperbolic space has received extensive attention because it can accurately and concisely represent hierarchical data. Currently, for knowledge graph completion tasks, the introduction of exogenous information of entities can enrich the knowledge representation of entities, but there is a problem that entities have different levels under different relations, and the embeddings of different entities in Euclidean space often requires high dimensional space to distinguish. Therefore, in order to solve the above problem, we propose a method that use entity descriptions to complete the knowledge gr

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49

Apanasov, Boris. "Quasiregular Mappings and Discrete Group Actions." Ukrainian Mathematical Bulletin 18, no. 4 (2021): 441–65. http://dx.doi.org/10.37069/1810-3200-2021-18-4-1.

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We develop a new tool based on quasiconformal dynamics and conformal dynamics of discrete group actions in 3-geometries to construct new types of quasiregular and quasisymmetric mappings in space. This tool has close relations to new effects in Teichmüller spaces of conformally flat structures on closed hyperbolic 3-manifolds/orbifolds and non-trivial hyperbolic 4-cobordisms, to the hyperbolic and conformal interbreedings as well as to non-faithful discrete representations of uniform hyperbolic 3-lattices. We demonstrate several applications of this tool and new types of quasiregular mappings

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50

Qiu, Chongyang, Xinfei Li, Jianhua Pang, and Peichang Ouyang. "Visualization of Escher-like Spiral Patterns in Hyperbolic Space." Symmetry 14, no. 1 (2022): 134. http://dx.doi.org/10.3390/sym14010134.

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Spirals, tilings, and hyperbolic geometry are important mathematical topics with outstanding aesthetic elements. Nonetheless, research on their aesthetic visualization is extremely limited. In this paper, we give a simple method for creating Escher-like hyperbolic spiral patterns. To this end, we first present a fast algorithm to construct Euclidean spiral tilings with cyclic symmetry. Then, based on a one-to-one mapping between Euclidean and hyperbolic spaces, we establish two simple approaches for constructing spiral tilings in hyperbolic models. Finally, we use wallpaper templates to render

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