Isotropic minimal immersions of spheres into spheres

Minimal Immersions of Symmetric Spaces into Spheres

Minimal Immersions of Spheres and Moduli

Minimal immersions of round spheres into round spheres, or spherical minimal immersions for short, or “spherical soap bubbles”, belong to a fast growing and fascinating area between algebra and geometry. This theory has rich interconnections with a variety of mathematical disciplines such as invariant theory, convex geometry, harmonic maps, and orthogonal multiplications. In this survey article...

On the Moduli of Isotropic and Helical Minimal Immersions between Spheres

DoCarmo-Wallach theory and its subsequent refinements assert the rich abundance of spherical minimal immersions, minimal immersions of round spheres into round spheres. A spherical minimal immersion can be written as a conformal minimal immersion f : Sm → SV with domain the Euclidean m-sphere Sm and range the unit sphere SV of a Euclidean vector space V . Takahashi’s theorem then implies that t...

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.

The Existence of Minimal Immersions of 2-Spheres