Relevant bibliographies by topics / Holomorphic quadratic differentials

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Holomorphic quadratic differentials'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Holomorphic quadratic differentials"

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Große, Nadine, and Melanie Rupflin. "Holomorphic quadratic differentials dual to Fenchel–Nielsen coordinates." Annals of Global Analysis and Geometry 55, no. 3 (November 16, 2018): 479–507. http://dx.doi.org/10.1007/s10455-018-9636-y.

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Kenyon, Richard, and Wai Yeung Lam. "Holomorphic quadratic differentials on graphs and the chromatic polynomial." Journal of Combinatorial Theory, Series A 170 (February 2020): 105140. http://dx.doi.org/10.1016/j.jcta.2019.105140.

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AU, THOMAS KWOK-KEUNG, and TOM YAU-HENG WAN. "PRESCRIBED HORIZONTAL AND VERTICAL TREES PROBLEM OF QUADRATIC DIFFERENTIALS." Communications in Contemporary Mathematics 08, no. 03 (June 2006): 381–99. http://dx.doi.org/10.1142/s0219199706002155.

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A sufficient condition for the existence of holomorphic quadratic differential on a non-compact simply-connected Riemann surface with prescribed horizontal and vertical trees is obtained. In particular, for any pair of complete ℝ-trees of finite vertices with (n + 2) infinite edges, there exists a polynomial quadratic differential on ℂ of degree n such that the associated vertical and horizontal trees are isometric to the given pair.
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Yao, Guowu. "A note on holomorphic quadratic differentials on the unit disk." Kodai Mathematical Journal 39, no. 1 (March 2016): 72–79. http://dx.doi.org/10.2996/kmj/1458651692.

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Fernández, Isabel, and Pablo Mira. "Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space." Transactions of the American Mathematical Society 361, no. 11 (June 22, 2009): 5737–52. http://dx.doi.org/10.1090/s0002-9947-09-04645-5.

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Chang, Zhe. "The Holomorphic Quadratic Differentials of Amplitudes for Strings with Boundaries." Communications in Theoretical Physics 13, no. 1 (January 1990): 49–56. http://dx.doi.org/10.1088/0253-6102/13/1/49.

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KIRSCHNER, R. "BOUNDARY REPARAMETRIZATIONS AS ADDITIONAL MODULI FOR THE STRING PROPAGATOR." Modern Physics Letters A 04, no. 03 (February 1989): 283–91. http://dx.doi.org/10.1142/s0217732389000356.

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Analyzing the Polyakov integral on surfaces with boundaries, where the values of the string variables are fixed, we use the observation that there are more holomorphic quadratic differentials besides those obtained as restrictions from the Schottky double. They are naturally related to boundary reparametrizations. The corresponding additional moduli are used to express the integration over metrices. Some details are given for the vacuum functional and the propagator.
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Matone, Marco, and Roberto Volpato. "Linear relations among holomorphic quadratic differentials and induced Siegel's metric on Mg." Journal of Mathematical Physics 52, no. 10 (October 2011): 102305. http://dx.doi.org/10.1063/1.3653550.

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Sugawa, Toshiyuki. "A conformally invariant metric on Riemann surfaces associated with integrable holomorphic quadratic differentials." Mathematische Zeitschrift 266, no. 3 (August 11, 2009): 645–64. http://dx.doi.org/10.1007/s00209-009-0590-z.

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ZHANG, C. "SINGULARITIES OF QUADRATIC DIFFERENTIALS AND EXTREMAL TEICHMÜLLER MAPPINGS DEFINED BY DEHN TWISTS." Journal of the Australian Mathematical Society 87, no. 2 (October 2009): 275–88. http://dx.doi.org/10.1017/s1446788709000032.

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AbstractLet S be a Riemann surface of finite type. Let ω be a pseudo-Anosov map of S that is obtained from Dehn twists along two families {A,B} of simple closed geodesics that fill S. Then ω can be realized as an extremal Teichmüller mapping on a surface of the same type (also denoted by S). Let ϕ be the corresponding holomorphic quadratic differential on S. We show that under certain conditions all possible nonpuncture zeros of ϕ stay away from all closures of once punctured disk components of S∖{A,B}, and the closure of each disk component of S∖{A,B} contains at most one zero of ϕ. As a consequence, we show that the number of distinct zeros and poles of ϕ is less than or equal to the number of components of S∖{A,B}.
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Dissertations / Theses on the topic "Holomorphic quadratic differentials"

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Sarkar, Amar Deep. "A Study of Some Conformal Metrics and Invariants on Planar Domains." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4910.

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The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. We will be interested in the invariants associated to the Carathéodory metric such as its higher-order curvatures that were introduced by Burbea and the Aumann-Carathéodory rigidity constant, the Sugawa metric and the Hurwitz metric. The basic technical step in all these is the method of scaling the domain near a smooth boundary point. To estimate the higher-order curvatures using scaling, we generalize an old theorem of Suita on the real analyticity of the Carathéodory metric on planar domains and in the process, we show convergence of the Szeg˝o and Garabedian kernels as well. By using similar ideas we also show that the Aumann-Carathéodory rigidity constant converges to 1 near smooth boundary points. Next on the line is a conformal metric defined using holomorphic quadratic differentials. Thiswas done by T. Sugawa andwe will refer to this as the Sugawa metric. It is shown that this metric is uniformly comparable to the quasi-hyperbolic metric on a smoothly bounded domain. We also study the Hurwitz metric that was introduced by D. Minda. Its construction is similar to the Kobayashi metric but the essential difference lies in the class of holomorphic maps that are considered in its definition. We show that this metric is continuous and also strengthen Minda’s theorem about its comparability with the quasi-hyperbolic metric by estimating the constants in a more natural manner. Finally, we get some weak estimates on the generalized upper and lower curvatures of the Sugawa and Hurwitz metrics.
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Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.

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The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge--Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.
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Books on the topic "Holomorphic quadratic differentials"

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Farb, Benson, and Dan Margalit. Teichmuller Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0012.

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This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.
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Book chapters on the topic "Holomorphic quadratic differentials"

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Gupta, Subhojoy. "Holomorphic quadratic differentials in Teichmüller theory." In Handbook of Teichmüller Theory, Volume VII, 89–124. Zuerich, Switzerland: European Mathematical Society Publishing House, 2020. http://dx.doi.org/10.4171/203-1/4.

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Kusunoki, Yukio. "Integrable holomorphic quadratic differentials with simple zeros." In Mathematical Sciences Research Institute Publications, 209–13. New York, NY: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-9602-4_19.

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Lam, Wai Yeung, and Ulrich Pinkall. "Holomorphic Vector Fields and Quadratic Differentials on Planar Triangular Meshes." In Advances in Discrete Differential Geometry, 241–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-50447-5_7.

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You might also be interested in the extended bibliographies on the topic 'Holomorphic quadratic differentials' for particular source types:
Journal articles
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