Gauss curvature estimates for minimal graphs

Maria Nowak, Magdalena Wołoszkiewicz

Abstract


We estimate the Gauss curvature of nonparametric minimal surfaces over the two-slit plane \(\mathbb{C}\setminus ((-\infty,-1]\cup [1,\infty))\) at points above the interval \((-1, 1)\).

Full Text:

PDF

References


Duren, P., Harmonic Mappings in the Plane, Cambridge Univ. Press, Cambridge, 2004.

Grigorian, A., Szapiel, W., Two-slit harmonic mappings, Ann. Univ. Mariae Curie-Skłodowska Sect. A 49 (1995), 59-84.

Hengartner, W., Schober, G., Curvature estimates for some minimal surfaces, Complex Analysis, Articles Dedicated to Albert Pfluger on the Occasion of his 80th Birthday, J. Hersch and A. Huber (eds.), Birh¨auser Verlag, Basel, 1988, pp. 87-110.

Jun, S. H., Curvature estimates for minimal surfaces, Proc. Amer. Math. Soc. 114 (1992), no. 2, 527-533.

Livingston, A. E., Univalent harmonic mappings II, Ann. Polon. Math. 67 (1997), no. 2, 131-145.




DOI: http://dx.doi.org/10.2478/v10062-011-0018-1
Date of publication: 2016-07-27 21:54:10
Date of submission: 2016-07-26 22:10:37


Statistics


Total abstract view - 737
Downloads (from 2020-06-17) - PDF - 404

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2011 Maria Nowak, Magdalena Wołoszkiewicz