1+1 Wave Maps into Symmetric Spaces

Maps into projective spaces

We compute the cohomology of the Picard bundle on the desingularization J̃ d (Y ) of the compactified Jacobian of an irreducible nodal curve Y . We use it to compute the cohomology classes of the Brill–Noether loci in J̃ d (Y ). We show that the moduli space M of morphisms of a fixed degree from Y to a projective space has a smooth compactification. As another application of the cohomology of the...

Summing Inclusion Maps between Symmetric Sequence Spaces

In 1973/74 Bennett and (independently) Carl proved that for 1 ≤ u ≤ 2 the identity map id: `u ↪→ `2 is absolutely (u, 1)-summing, i. e., for every unconditionally summable sequence (xn) in `u the scalar sequence (‖xn‖`2 ) is contained in `u, which improved upon well-known results of Littlewood and Orlicz. The following substantial extension is our main result: For a 2-concave symmetric Banach s...

Hypergroups, Symmetric Spaces, and Wrapping Maps

This paper attempts an exposition of the connection between symmetric spaces and hypergroup theory. This connection is not new to those involved in hypergroups, as the classical symmetric spaces have always provided a very rich source of examples for the theory. However for those working in symmetric spaces, the usefulness of the hypergroup point of view may not be well known. It provides a new...

Stability of Spherically Symmetric Wave Maps

We study Wave Maps from R2+1 to the hyperbolic plane H2 with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some H1+μ, μ > 0. We show that such Wave Maps don’t develop singularities in finite time and stay close to the Wave Map extending the spherically symmetric data(whose existence is ensured by a theorem of Christodoulou-T...

Minimal Immersions of Symmetric Spaces into Spheres