Stability of harmonic maps and standard minimal immersions

Moduli for Spherical Maps and Minimal Immersions of Homogeneous Spaces

The DoCarmo-Wallach theory studies isometric minimal immersions f : G/K → S of a compact Riemannian homogeneous space G/K into Euclidean n -spheres for various n . For a given domain G/K , the moduli space of such immersions is a compact convex body in a representation space for the Lie group G . In 1971 DoCarmo and Wallach gave a lower bound for the (dimension of the) moduli for G/K = S , and ...

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 ...

Minimal submanifolds and harmonic maps through multitime maximum principle

Some optimization problems arising Differential Geometry, as for example, the minimal submanifolds problem and the harmonic maps problem are solved here via interior solutions of appropriate multitime optimal control techniques. Similar multitime optimal control problems can be found in Material Strength, Fluid Mechanics, Magnetohydrodynamics etc. Firstly, we summarize the tools of our recent d...

Contact Structures and Harmonic Maps with Minimal Fibres

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...