On minimal immersions of R2 into SN

Minimal Immersions of Symmetric Spaces into Spheres

Minimal Immersions of Kähler Manifolds into Euclidean Spaces

We prove that a minimal isometric immersion of a Kähler-Einstein or homogeneous Kähler manifold into an Euclidean space must be totally geodesic. As an application we show that an open subset of the real hyperbolic plane RH2 cannot be minimally immersed into the Euclidean space. As another application we prove that if an irreducible Kähler manifold is minimally immersed in an Euclidean space th...

Compact Complete Minimal Immersions In

ANTONIO ALARC´ON ABSTRACT. In this paper we construct complete minimal surfaces with boundary in R 3 of arbitrary finite topology. For any arbitrary finite topological type we find a compact Riemann surface M, an open domain M ⊂ M with the fixed topological type, and a conformal complete minimal immersion X : M → R 3 which can be extended to a continuous map X : M → R 3 , such that X |∂M is an ...

Spherical Minimal Immersions of Spherical Space Forms

Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ:M → S(r) ⊂ R is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace operator on M for the same eigenvalue. And conve...

Spherical Minimal Immersions of the 3-sphere

In 1966 Takahashi [11] proved that a minimal isometric immersion f : S(1) → S(r) of round spheres exists iff r = √ m/λp, where λp is the pth eigenvalue of the Laplacian on S; in this case, the components of f are spherical harmonics on S of order p. This immersion is unique up to congruence on the range and agrees with the generalized Veronese map if m = 2 as was shown in 1967 by Calabi [1]. In...