Singularities of energy minimizing maps from the ball to the sphere: Examples, counterexamples, and bounds
The paper studies the singularities of Dirichlet's integral energy upon the mappings from a domain in \(R^ 3\) to \(S^ 2\) with prescribed boundary value functions. The main result in the first part of the paper states that the number of singular points of such a minimizer is linearly dominated by the boundary energy. The second part of the paper is devoted to ``the curious behaviour of singularities''. It is shown that, within an open ball in \(R^ 3\), the minimizers with zero boundary mapping area can have arbitrarily many singularities. It is then constructed a boundary function having a symmetry about the equator in a ball for which every minimizer possesses unsymmetric singularities. Many other interesting results are proved.
scientific article; zbMATH DE number 4102119