Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 2

On quasiconformal harmonic mappings lifting to minimal surfaces

Sayfa
267–277
Yayın Tarihi
2022-11-04
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also obtain some estimates of the Gaussian curvature of the minimal surfaces in 3-dimensional Euclidean space R3 and of the spacelike minimal surfaces in L3.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:We prove a growth theorem for a function to belong to the class \sum(m;a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L3.
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Temel Bulgular & Veri:We prove a growth theorem for a function to belong to the class \sum(m;a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L3.
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Sonuç & Katkı:We also obtain some estimates of the Gaussian curvature of the minimal surfaces in 3-dimensional Euclidean space R3 and of the spacelike minimal surfaces in L3.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Minimal surface · isothermal parameters · Weierstrass-Enneper representation

Özet

We prove a growth theorem for a function to belong to the class \sum(m;a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L3. We also obtain some estimates of the Gaussian curvature of the minimal surfaces in 3-dimensional Euclidean space R3 and of the spacelike minimal surfaces in L3.

Abstract

We prove a growth theorem for a function to belong to the class \sum(m;a) and generalize a Weierstrass-Enneper representation type theorem for the minimal surfaces given in [5] to spacelike minimal surfaces which lie in 3-dimensional Lorentz-Minkowski space L3. We also obtain some estimates of the Gaussian curvature of the minimal surfaces in 3-dimensional Euclidean space R3 and of the spacelike minimal surfaces in L3.

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Bu Makaleye Atıf Yap

TAŞTAN, H. M., POLATOĞLU, Y. (2022). On quasiconformal harmonic mappings lifting to minimal surfaces. Turkish Journal of Mathematics, Cilt: 37 - Sayı: 2, 267–277. https://ajindex.com/articles/608355

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Kaynakça (10)

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  2. Chuaqui, M., Duren, P. and Osgood, B.: The Schwarzian derivative for harmonic mappings, J. Analyse Math. 91, 329–351 (2003).
  3. Dey, R.: The Weierstrass-Enneper representation using hodographic coordinates on a minimal surface, Proc. Indian Acad. Sci.(Math.Sci) 113, No. 2, 189–193 (2003).
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  5. Duren, P.: Harmonic mappings in the plane, Cambridge University Press, Cambridge U.K, 2004. Ferr´ andez, A. and Lucas, P.: On surfaces in the 3-dimensional Lorentz-Minkowski space, Pacific J. Math. 152, No. 1, 93–100 (1992).
  6. Kalaj, D.: Quasiconformal harmonic mappings and close-to-convex domains, Filomat 24, No. 1, 63–68 (2010).
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  8. Lehto, O., Virtanen, K. I.: Quasiconformal mappings in the plane, Second edition. Translated from the German by Lucas, K.W. Die Grundlehren der mathematischen Wissenhaften, Band 126. Springer-Verlag, New York-Heidelberg, 19 Lewandoski, Z.: Starlike madorants and subordination, Annales Universitatis, Mariae-Curie Sklodowska, LublinPolonia, XV. Sectio A, 79–84 (1961).
  9. Lira, J. H., Melo, M. and Mercuri, M.: A Weierstrass representation for minimal surfaces in 3-dimensional manifolds, Results. Math. 60, 311–323 (2011).
  10. Martio, O.: On harmonic quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I No. 425, 3–10 (1968). Ta¸stan, H. M. and Polato˘ glu, Y.: Growth properties for Weierstrass-Enneper representation of a minimal surface, Acta Universitatis Apulensis 20, 55–62 (2009).