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Extremal length and Dirichlet problem on Klein surfaces

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Języki publikacji
EN
Abstrakty
EN
The object of this paper is to extend the method of extremal length to Klein surfaces by solving conformally invariant extremal problems on the complex double. Within this method we define the extremal length, the extremal distance, the conjugate extremal distance, the modulus, the reduced extremal distance on a Klein surface and we study their dependences on arcs.
Słowa kluczowe
Rocznik
Strony
281--296
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • University of Craiova Department of Mathematics Street A.I. Cuza No 13, Craiova 200585, Romania
Bibliografia
  • [1] L.V. Ahlfors, Conformal Invariants: Topics in Geometric Function Theory, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Dusseldorf-Johannesburg, 1973.
  • [2] L. Ahlfors, A. Beurling, Conformal invariants and function-theoretic null-sets, Acta Math. 83 (1950), 101-129.
  • [3] L.V. Ahlfors, L. Sario, Riemann Surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960.
  • [4] N.L. Ailing, N. Greenleaf, Foundations of the Theory of Klein Surfaces, Lecture Notes in Math. 219, Springer-Verlag, 1971.
  • [5] C. Andreian Cazacu, On morphisms of Klein surfaces, Rev. Roumaine Math. Pures Appl. 31 (1986) 6, 461-470.
  • [6] S.S. Antman, Fundamental Mathematical Problems in the Theory of Nonlinear Elasticity, North-Holland, (1976), 33-54.
  • [7] J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal. 63 (1977), 337-403.
  • [8] I. Barza, Integration on Nonorientable Riemann Surfaces, [in:] Almost Complex Structures, World Scientific, Singapore-New Jersey-London-Hong Kong, 1995, 63-97.
  • [9] I. Barza, D. Ghi§a, Explicit formulas for Green's functions on the annulus and on the Mobius strip, Acta Applicandae Mathematicae 54 (1998), 289-302.
  • [10] E. Bujalance, J.J. Etayo, J.M. Gamboa, G. Gromadzki, Automorphisms Groups of Compact Bordered Klein Surfaces, A Combinatorial Approach, Lecture Notes in Math., vol. 1439, Springer-Verlag, 1990.
  • [11] J. Jenkins, Univalent functions and conformal mapping, Springer, Berlin, 1958, 13-14.
  • [12] S.G. Krantz, Partial Differential Equations and Complex Analysis, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.
  • [13] R. Nevanlinna, Analytic Functions, Springer-Verlag, Berlin, 1970.
  • [14] Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, Cambridge, 2005.
  • [15] B. Rodin, L. Sario, Principal functions, Van Nostrand, Princeton, N.J., 1968.
  • [16] M. Rosju, Harmonic measures and Poisson kernels on Klein surfaces, Electronic Journal of Differential Equations 2017 (2017) 269, 1-7.
  • [17] L. Sario, K. Oikawa, Capacity functions, Die Grundlehren der math. Wissenschaften, Band 149, Springer-Verlag, New York, 1969.
  • [18] M. Schiffer, D. Spencer, Functionals of Finite Riemann Surfaces, Princeton University Press, 1954.
  • [19] M. Seppala, T. Sorvali, Geometry of Riemann Surfaces and Teichmuller Spaces, North-Holland Mathematics Studies, vol. 169, North-Holland, Amsterdam, 1992.
  • [20] J. Serrin, Removable singularities of solutions of elliptic equations, Arch. Rational Mech. Anal. 17 (1964), 67-78.
  • [21] J. Serrin, Local behavior of solutions of quasilinear equations, Acta Math. Ill (1964), 247-302.
  • [22] O. Teichmuller, Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. Preuss. Akad. Wiss., Math.-Naturw. Kl. 1940, No. 22, 1-197, 1940. English translation by G. Theret, Extremal quasiconformal mappings and quadratic differentials [in:] Handbook of Teichmuller theory, A. Papadopoulos (ed.), vol. V, EMS Publishing House, 321-484, 2015.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-bb9d1883-1f2d-47ef-9bf3-e4de4accfac5
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