On solving the Plateau problem in parametric form.
Cahlon, Baruch, Solomon, Alan D., Nachman, Louis J. (1983)
International Journal of Mathematics and Mathematical Sciences
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Cahlon, Baruch, Solomon, Alan D., Nachman, Louis J. (1983)
International Journal of Mathematics and Mathematical Sciences
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Jih-Hsin Cheng, Jenn-Fang Hwang, Andrea Malchiodi, Paul Yang (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface...
Eugenio Aulisa, Magdalena Toda, Zeynep Kose (2013)
Open Mathematics
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Isothermic parameterizations are synonyms of isothermal curvature line parameterizations, for surfaces immersed in Euclidean spaces. We provide a method of constructing isothermic coordinate charts on surfaces which admit them, starting from an arbitrary chart. One of the primary applications of this work consists of numerical algorithms for surface visualization.
Robert Finn (1984)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Johannes C. C. Nitsche (1976)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Jürgen Jost (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Malkowsky, Eberhard, Veličković, Vesna (2008)
APPS. Applied Sciences
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Jorge Sotomayor, Dirk Siersma, Ronaldo Garcia (1999)
Banach Center Publications
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This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane, established by Siersma [3]. In the present case a conflict surface arises, equidistant from the given convex sets. The Gaussian, mean curvatures and the location of umbilic points on the conflict surface are determined here. Initial results on the Darbouxian type of umbilic points on conflict surfaces are also established. The results are expressed in terms of...