On the uniqueness of minimizing harmonic maps to a closed hemisphere

We study the uniqueness of minimizing harmonic maps to a closed hemisphere. We are able to describe the boundary data for which there are more than one minimizer, and to describe in these cases the corresponding set of minimizers. This is a limiting case for a former result of W.Jäger and H.Kaul.This article was processed by the author using the Springer-Verlag T_EX PJourlg macro package 1991.     

Distances between classes in $$W^{1,1}(\Omega ;{\mathbb {S}}^{1})$$

We introduce an equivalence relation on the space \(W^{1,1}(\Omega ;{\mathbb {S}}^1)\) which classifies maps according to their “topological singularities”. We establish sharp bounds for the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. Similar questions are examined for the space \(W^{1,p}(\Omega ;{\mathbb {S}}^1)\) when \(p>1\).     

Polynomiality of invariants, unimodularity and adapted pairs

Let \mathfraka \mathfrak{a} be a finite-dimensional Lie algebra and Y( \mathfraka ) Y\left( \mathfrak{a} \right) the \mathfraka \mathfrak{a} invariant subalgebra of its symmetric algebra S( \mathfraka ) S\left( \mathfrak{a} \right) under adjoint action. Recently there has been considerable interest in studying situations when Y( \mathfraka ) Y\left( \mathfrak{a} \right) may be polynomial on index \mathfraka \mathfrak{a} generators, for example if \mathfraka \mathfrak{a} is a biparabolic or a centralizer \mathfrakg^x {\mathfrak{g}^x} in a semisimple Lie algebra \mathfrakg \mathfrak{g} .     

Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part II

(Accepted July 23, 1996)     

The distance between homotopy classes of <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-valued maps in multiply connected domains

Certain Sobolev spaces of S ¹-valued functions can be written as a disjoint union of homotopy classes. The problem of finding the distance between different homotopy classes in such spaces is considered. In particular, several types of one-dimensional and two-dimensional domains are studied. Lower bounds are derived for these distances. Furthermore, in many cases it is shown that the lower bounds are sharp but are not achieved. The first author’s work of was supported in part by NSF grant 0503887. The second author’s research of was supported by G.S. Elkin research fund.     

On a minimization problem with a mass constraint involving a potential vanishing on two curves

We study a singular perturbation type minimization problem with a mass constraint over a domain in ℝ ^N , involving a potential vanishing on two curves in the plane. We demonstrate how the behavior of the minimizers depends on the geometry of the domain and, more precisely, on its isoperimetric profile.     

Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part I

(Accepted July 23, 1996)     

Theorems of ergodic type for ρ-nonexpansive mappings in the Hilbert ball

Summary We present two types of ergodic theorems for contractive iterations in the Hilbert ball. Both explicit and implicit iterations are discussed.