Curvatures of surfaces associated with holomorphic functions
Richard Jerrard (1970)
Colloquium Mathematicae
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Richard Jerrard (1970)
Colloquium Mathematicae
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K. Leschke, K. Moriya (2016)
Complex Manifolds
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In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the...
Norio Ejiri (1994)
Compositio Mathematica
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Claudio Arezzo (2000)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Manhart, Friedrich (2009)
Beiträge zur Algebra und Geometrie
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James Carrell, Alan Howard, Czes Kosniowski (1973)
Mathematische Annalen
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Clifford J. Earle, Robert S. Fowler (1985)
Mathematische Annalen
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Adolfo Guillot (2014)
Annales de l’institut Fourier
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We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is compact). We also prove that, in a singular Stein surface endowed with a complete holomorphic vector field, a singular point of the surface where the zeros of the vector field do not accumulate is either a quasihomogeneous or a cyclic quotient singularity....
Francisco J. López, Francisco Martín (1999)
Publicacions Matemàtiques
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In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space.
H. Karcher (1988)
Manuscripta mathematica
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Shing-Tung Yau, William W. Meeks (1982)
Mathematische Zeitschrift
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