A note on stability of minimal surfaces in -dimensional hyperbolic space .
Li, Haizhong (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Li, Haizhong (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Alexander G. Reznikov (1992)
Publicacions Matemàtiques
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We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.
Renato de Azevedo Tribuzy, Irwen Valle Guadalupe (1985)
Rendiconti del Seminario Matematico della Università di Padova
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Harold Rosenberg (1991-1992)
Séminaire Bourbaki
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Rossman, Wayne, Sato, Katsunori (1998)
Experimental Mathematics
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Ricardo Sa Earp, Eric Toubiana (2000-2001)
Séminaire de théorie spectrale et géométrie
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Michael T. Anderson (1985)
Annales scientifiques de l'École Normale Supérieure
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Irwen Valle Guadalupe (1995)
Rendiconti del Seminario Matematico della Università di Padova
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Katsuei Kenmotsu (1997)
Archivum Mathematicum
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In this paper, history of reserches for minimal immersions from constant Gaussian curvature 2-manifolds into space forms is explained with special emphasis of works of O. Borůvka. Then recent results for the corresponding probrem to classify minimal immersions of such surfaces in complex space forms are discussed.