Relevant bibliographies by topics / Quasiconformal mappings in the plane

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

Academic literature on the topic 'Quasiconformal mappings in the plane'

Author: Grafiati
Published: 4 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Quasiconformal mappings in the plane"

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CHEN, XINGDI, and YUQIN QUE. "QUASICONFORMAL EXTENSIONS OF HARMONIC MAPPINGS WITH A COMPLEX PARAMETER." Journal of the Australian Mathematical Society 102, no. 3 (2016): 307–15. http://dx.doi.org/10.1017/s1446788716000355.

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In this paper, we study quasiconformal extensions of harmonic mappings. Utilizing a complex parameter, we build a bridge between the quasiconformal extension theorem for locally analytic functions given by Ahlfors [‘Sufficient conditions for quasiconformal extension’, Ann. of Math. Stud.79 (1974), 23–29] and the one for harmonic mappings recently given by Hernández and Martín [‘Quasiconformal extension of harmonic mappings in the plane’, Ann. Acad. Sci. Fenn. Math.38 (2) (2013), 617–630]. We also give a quasiconformal extension of a harmonic Teichmüller mapping, whose maximal dilatation estima
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Gutlyanskii, V. Ya, O. V. Nesmelova, and V. I. Ryazanov. "Semilinear equations in a plane and quasiconformal mappings." Reports of the National Academy of Sciences of Ukraine, no. 1 (February 16, 2017): 10–16. http://dx.doi.org/10.15407/dopovidi2017.01.010.

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Duka, Anila, and Ndriçim Sadikaj. "Quasiregular mapping that preserves plane." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 9 (2016): 6603–7. http://dx.doi.org/10.24297/jam.v12i9.131.

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Quasiregular mappings are a natural generalization of analytic functions to higher dimensions. Quasiregular mappings have many properties. Our work in this paper is to prove the following theorem: If f  a b is a quasiregular mapping which maps the plane onto the plane, then f is a bijection. We do this by finding the connection between quasiregular and quasiconformal mappings.
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Anderson, G. D., M. K. Vamanamurthy, and M. Vuorinen. "Distortion functions for plane quasiconformal mappings." Israel Journal of Mathematics 62, no. 1 (1988): 1–16. http://dx.doi.org/10.1007/bf02767349.

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Kurihara, Shigenori, and Shinji Yamashita. "Extremal functions for plane quasiconformal mappings." Journal of Mathematics of Kyoto University 43, no. 1 (2003): 71–99. http://dx.doi.org/10.1215/kjm/1250283741.

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Gartland, Chris, Derek Jung, and Matthew Romney. "Quasiconformal mappings on the Grushin plane." Mathematische Zeitschrift 287, no. 3-4 (2017): 915–28. http://dx.doi.org/10.1007/s00209-017-1851-x.

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Zhang, Xiaohui, Gendi Wang, Yuming Chu, and Songliang Qiu. "Distortion theorems of plane quasiconformal mappings." Journal of Mathematical Analysis and Applications 324, no. 1 (2006): 60–65. http://dx.doi.org/10.1016/j.jmaa.2005.11.066.

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Adamowicz, Tomasz, and María J. González. "Hardy Spaces for Quasiregular Mappings and Composition Operators." Journal of Geometric Analysis 31, no. 11 (2021): 11417–27. http://dx.doi.org/10.1007/s12220-021-00687-0.

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AbstractWe define Hardy spaces $${\mathcal {H}}^p$$ H p for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 i
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Manojlovic, Vesna. "Bi-lipschicity of quasiconformal harmonic mappings in the plane." Filomat 23, no. 1 (2009): 85–89. http://dx.doi.org/10.2298/fil0901085m.

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Hernández, Rodrigo, and María J. Martín. "Quasiconformal extension of harmonic mappings in the plane." Annales Academiae Scientiarum Fennicae Mathematica 38 (June 2013): 617–30. http://dx.doi.org/10.5186/aasfm.2013.3824.

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Dissertations / Theses on the topic "Quasiconformal mappings in the plane"

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Mercer, Nathan T. "Quasiconformal mappings in the complex plane." Virtual Press, 2006. http://liblink.bsu.edu/uhtbin/catkey/1348866.

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It is well known that, as a consequence of the Identity Theorem, we cannot "glue" together two analytic functions to create a new globally analytic function. In this paper we will both introduce and investigate special homeomorphisms, called quasiconformal maps, that are generalizations of the well known conformal maps. We will show that quasiconformal maps make this "gluing," up to conjugation, possible. Quasiconformal maps are a valuable tool in the field of complex dynamics. We will see how quasiconformal maps of infinitesimal circles have an image of an infinitesimal ellipse. Although quas
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Medwid, Mark Edward. "Rigidity of Quasiconformal Maps on Carnot Groups." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1497620176117104.

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Prats, Soler Martí. "Singular integral operators on sobolev spaces on domains and quasiconformal mappings." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/314193.

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En aquesta tesi s’obtenen nous resultats sobre l’acotació d’operadors de Calderón-Zygmund en espais de Sobolev en dominis de Rd. En primer lloc es demostra un teorema de tipus T(P) vàlid per a Wn,p(U), a on U és un domini uniforme acotat de Rd, n és un nombre natural arbitrari, i p>d. Essencialment, el resultat obtingut afirma que un operador de Calderón-Zygmund de convolució és acotat en aquest espai si i solament si per a tot polinomi P de grau menor que n restringit al domini, T(P) pertany a Wn,p(U). Per a índexs p menors o iguals que d, es demostra una condició suficient per a l'acotac
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Ohtake, Hiromi. "ON THE DEFORMATION OF FUCHSIAN GROUPS BY QUASICONFORMAL MAPPINGS WITH PARTIALLY VANISHING BELTRAMI COEFFICIENTS." 京都大学 (Kyoto University), 1988. http://hdl.handle.net/2433/86389.

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Villanueva, Segovia Cristina. "Properties of Lipschitz quotient mappings on the plane." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8266/.

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In the present work, we are concerned with the relation between the Lipschitz and co-Lipschitz constants of a mapping f : R2 → R2 and the cardinality of the inverse image of a point under the mapping f, depending on the norm on R2. It is known that there is a scale of real numbers 0 < ... < Pn <...< P1 < 1 such that for any Lipschitz quotient mapping from the Euclidean plane to itself, if the ratio between the co-Lipschitz and Lipschitz constants of f is bigger than Pn, then the cardinality of any fibre of f is less than or equal to n. Furthermore, it is proven that for the Euclidean case the
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Meyer, Daniel. "Melting snowballs /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5796.

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Maricato, José Benedito Jorge. "Uma abordagem para classificação de funções k-quaseconformes /." São José do Rio Preto : [s.n.], 2005. http://hdl.handle.net/11449/94298.

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Orientador: José Marcio Machado<br>Banca: Gilberto Aparecido Pratavieira<br>Banca: Manoel Ferreira Borges Neto<br>Resumo: As funções hipercomplexas do tipo zn, n natural, têm uma dilatação linear K uniformemente limitada em um domínio simplesmente conexo D, então podem ser classificadas de funções K-quaseconformes. Procuramos aqui quantificar K e verificar suas dependências. Para tanto, as generalizações de zn foram necessárias e obtidas, originando para z escrito em coordenadas esféricas, polinômios em função de um raio r.<br>Abstract: The hypercomplex functions of zn type, natural n, have a
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Nisbet, Kenneth Charles. "Dynamics of mappings of the plane and of the circle." Thesis, University of Edinburgh, 1989. http://hdl.handle.net/1842/15533.

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Fryer, Robert Neil. "Dynamics of degree two quasiregular mappings of the plane of constant dilatation." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/54680/.

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Let h : C ! C be an R-linear map. In this thesis, we explore the dynamics of the quasiregular mapping h(z)2 + c. It is well-known that a polynomial can be conjugated by a holomorphic map to w 7! wd in a neighbourhood of infinity. This map is called a Böttcher coordinate for f near infinity. We construct a Böttcher type coordinate for compositions of h and polynomials, a class of mappings first studied in [19]. As an application, we prove that if h is affne and c 2 C, then h(z)2 + c is not uniformly quasiregular. Via the Böttcher type coordinate, we are able to obtain results for any degree two
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Maricato, José Benedito Jorge [UNESP]. "Uma abordagem para classificação de funções k-quaseconformes." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/94298.

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Made available in DSpace on 2014-06-11T19:27:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-12-16Bitstream added on 2014-06-13T20:08:14Z : No. of bitstreams: 1 maricato_jbj_me_sjrp.pdf: 3533133 bytes, checksum: 49d5a66024e9a9093dce4e46a4799314 (MD5)<br>As funções hipercomplexas do tipo zn, n natural, têm uma dilatação linear K uniformemente limitada em um domínio simplesmente conexo D, então podem ser classificadas de funções K-quaseconformes. Procuramos aqui quantificar K e verificar suas dependências. Para tanto, as generalizações de zn foram necessárias e obtidas, originando pa
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Books on the topic "Quasiconformal mappings in the plane"

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author, Gutlyanskii Vladimir, Martio O. (Olli) author, and Ryazanov Vladimir author, eds. Infinitesimal geometry of quasiconformal and bi-Lipschitz mappings in the plane. European Mathematical Society Publishing House, 2013.

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Tadeusz, Iwaniec, and Martin Gaven, eds. Elliptic partial differential equations and quasiconformal mappings in the plane. Princeton University Press, 2009.

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Vuorinen, Matti, ed. Quasiconformal Space Mappings. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094234.

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Lectures on quasiconformal mappings. 2nd ed. American Mathematical Society, 2006.

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Ahlfors, Lars. Lectures on Quasiconformal Mappings. American Mathematical Society, 2006. http://dx.doi.org/10.1090/ulect/038.

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Duren, Peter, Juha Heinonen, Brad Osgood, and Bruce Palka, eds. Quasiconformal Mappings and Analysis. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0605-7.

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Ahlfors, Lars Valerian. Lectures on quasiconformal mappings. Wadsworth & Brooks/Cole Advanced Books & Software, 1987.

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Quasiregular mappings. Springer-Verlag, 1993.

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Grigorʹevich, Reshetni͡a︡k I͡U︡riĭ, ed. Quasiconformal mappings and Sobolev spaces. Kluwer Academic Publishers, 1990.

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Gol’dshtein, V. M., and Yu G. Reshetnyak. Quasiconformal Mappings and Sobolev Spaces. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1922-8.

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Book chapters on the topic "Quasiconformal mappings in the plane"

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Earle, Clifford J., and Li Zhong. "Extremal Quasiconformal Mappings in Plane Domains." In Quasiconformal Mappings and Analysis. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0605-7_10.

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Imayoshi, Yoichi, and Masahiko Taniguchi. "Quasiconformal Mappings." In An Introduction to Teichmüller Spaces. Springer Japan, 1994. http://dx.doi.org/10.1007/978-4-431-68174-8_4.

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Lehto, Olli. "Quasiconformal Mappings." In Graduate Texts in Mathematics. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4613-8652-0_2.

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Gardiner, Frederick, and Nikola Lakic. "Earthquake mappings." In Quasiconformal Teichmüller Theory. American Mathematical Society, 1999. http://dx.doi.org/10.1090/surv/076/18.

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Anderson, G. D., M. K. Vamanamurthy, and M. Vuorinen. "Conformal invariants, quasiconformal maps, and special functions." In Quasiconformal Space Mappings. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094235.

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Gehring, F. W. "Topics in quasiconformal mappings." In Quasiconformal Space Mappings. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094236.

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Iwaniec, Tadeusz. "L p -theory of quasiregular mappings." In Quasiconformal Space Mappings. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094237.

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Martio, Olli. "Partial differential equations and quasiregular mappings." In Quasiconformal Space Mappings. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094238.

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Reshetnyak, Yu G. "On functional classes invariant relative to homotheties." In Quasiconformal Space Mappings. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094239.

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Rickman, Seppo. "Picard’s theorem and defect relation for quasiregular mappings." In Quasiconformal Space Mappings. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094240.

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Conference papers on the topic "Quasiconformal mappings in the plane"

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Golberg, A. "Spatial quasiconformal mappings and directional dilatations." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_0006.

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Aydoğan, Melike, and Yaşar Polatoğlu. "Quasiconformal harmonic mappings related to Janowski alpha-spirallike functions." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882574.

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GOLBERG, ANATOLY. "GEOMETRIC APPROACH IN THE THEORY OF GENERALIZED QUASICONFORMAL MAPPINGS." In Proceedings of the Conference Satellite to ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812778833_0013.

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MIKLYUKOV, V. M. "SPEED OF APPROXIMATION TO DEGENERATE QUASICONFORMAL MAPPINGS AND STABILITY PROBLEMS." In Proceedings of the Conference Satellite to ICM 2006. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812778833_0003.

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"Haptic Rendering using Support Plane Mappings." In International Conference on Computer Graphics Theory and Applications. SCITEPRESS - Science and and Technology Publications, 2014. http://dx.doi.org/10.5220/0004680604450452.

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Bomba, Andrii, and Kateryna Malash. "Modeling the Formation of Craters caused by the Two Charges Explosion using Quasiconformal Mappings Numerical Methods." In 2019 9th International Conference on Advanced Computer Information Technologies (ACIT). IEEE, 2019. http://dx.doi.org/10.1109/acitt.2019.8780021.

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Rastgoftar, Hossein, and Suhada Jayasuriya. "Evolution of Multi Agent Systems Under a New Communication Topology." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6140.

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In this paper, a multi agent system (MAS) is considered as particles of a continuum deforming under a specific class of homeomorphic mappings, called a homogenous transformation. We have recently showed how a desired homogenous mapping of the MAS in a n–D space can be prescribed by transient positions of n + 1 leaders placed at the vertices of a n–D polytope, called leading polytope [1–9]. In this article, we first minimize the acceleration norm with (i) initial and final positions of the leaders known and (ii) leaders (located at the vertices of the leading polytope) are constrained to move i
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