On minimal immersions in Finsler space

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...

Minimal Lagrangian isotropic immersions in indefinite complex space forms

Eigenmaps and the Space of Minimal Immersions between Spheres

In 1971 DoCarmo and Wallach gave a lower bound for the dimension of the space of minimal immersions between spheres and they believed that the lower estimate was sharp. We give here a different approach using conformal fields and eigenmaps; determine the exact dimension of this space and conclude that their conjecture is true.

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 ...

Critical Points of the Distance Function on the Moduli Space for Spherical Eigenmaps and Minimal Immersions

The boundary of a DoCarmo-Wallach moduli space parametrizing (harmonic) eigenmaps between spheres or spherical minimal immersions carries a natural stratification. In this paper we study the critical points of the distance function on the boundary strata. We show that the critical points provide a natural generalization of eigenmaps with L-orthonormal components. We also point out that many cla...