Minimal deformation of a non-full minimal surface in $S^4(1)$

Norio Ejiri

Displaying similar documents to “Minimal deformation of a non-full minimal surface in $S^{4} (1)$ ”

Minimal surfaces and deformations of holomorphic curves in Kähler-Einstein manifolds

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Applications of Quaternionic Holomorphic Geometry to minimal surfaces

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...

The holomorphic contractibility of two generalized Teichmüller spaces.

Earle, Clifford J. (2004)

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Linearization and explicit solutions of the minimal surface equations.

Alexander G. Reznikov (1992)

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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.