Startseite Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
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Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1

  • Si Duc Quang EMAIL logo und Do Thi Thuy Hang
Veröffentlicht/Copyright: 14. November 2024
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Georgian Mathematical Journal
Aus der Zeitschrift Georgian Mathematical Journal Band 32 Heft 3

Abstract

Let S 1 , S 2 , S 3 be oriented non-flat minimal surfaces immersed in ℝ n + 1 ( n ≥ 2 ) with the Gauss maps G 1 , G 2 , G 3 into ℙ n ⁢ ( ℂ ) , respectively. Assume that there are conformal diffeomorphisms Φ 2 , Φ 3 of S 1 onto S 2 , S 3 respectively and let f 1 = G 1 , f 2 = G 2 ∘ Φ 2 , f 3 = G 3 ∘ Φ 3 . In this paper, we will show that f 1 , f 2 , f 3 are algebraic dependence, i.e., f 1 ∧ f 2 ∧ f 3 ≡ 0 , if they have the same inverse images for a few hyperplanes of ℙ n ⁢ ( ℂ ) in general position with some certain conditions.

Keywords: Gauss map; value distribution; holomorphic map; uniqueness; algebraic dependence; hyperplane
MSC 2020: 53A10; 53C42

References

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Received: 2024-01-22
Revised: 2024-05-29
Accepted: 2024-06-12
Published Online: 2024-11-14
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Some results in prime rings involving endomorphisms
  3. On the generalized fractional Laplace–Bessel operator
  4. Smoothness of solutions of differential equations of constant strength in Roumieu spaces
  5. Rings additively generated by certain periodic elements
  6. Rings whose clean elements are uniquely strongly clean
  7. New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications
  8. On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces
  9. Characterization of multiplicative Jordan n-higher derivations on unital rings
  10. The multiplicative Lie algebra on general linear groups
  11. The optimal control problem for systems of integro-differential equations with finite and infinite horizon
  12. Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
  13. Nonlinear mixed Jordan-type derivations on *-algebras
  14. SG pseudo-differential operators in Dunkl setting
  15. Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
  16. The binary products of algebras with genetic realization
  17. A relationship between the structure of a quotient ring and * -identities involving pair of derivations
https://doi.org/10.1515/gmj-2024-2066
Schlagwörter für diesen Artikel
Gauss map; value distribution; holomorphic map; uniqueness; algebraic dependence; hyperplane

Artikel in diesem Heft

  1. Frontmatter
  2. Some results in prime rings involving endomorphisms
  3. On the generalized fractional Laplace–Bessel operator
  4. Smoothness of solutions of differential equations of constant strength in Roumieu spaces
  5. Rings additively generated by certain periodic elements
  6. Rings whose clean elements are uniquely strongly clean
  7. New norm inequalities for Jensen’s gap of analytic functions in Banach algebras with applications
  8. On a nonlinear general eigenvalue problem in Musielak–Orlicz spaces
  9. Characterization of multiplicative Jordan n-higher derivations on unital rings
  10. The multiplicative Lie algebra on general linear groups
  11. The optimal control problem for systems of integro-differential equations with finite and infinite horizon
  12. Algebraic dependence of the Gauss maps on minimal surfaces immersed in ℝ n+1
  13. Nonlinear mixed Jordan-type derivations on *-algebras
  14. SG pseudo-differential operators in Dunkl setting
  15. Exploring the properties of multivariable Hermite polynomials in relation to Apostol-type Frobenius–Genocchi polynomials
  16. The binary products of algebras with genetic realization
  17. A relationship between the structure of a quotient ring and * -identities involving pair of derivations
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