Page 1

Displaying 1 – 12 of 12

Showing per page

Simultaneous unitarizability of SL n -valued maps, and constant mean curvature k-noid monodromy

Wayne Rossman, Nicholas Schmitt (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into SL n under conjugation by a single analytic matrix map.We apply this result to the monodromy arising from an integrable partial differential equation to construct a family of k -noids, genus-zero constant mean curvature surfaces with three or more ends in euclidean, spherical and hyperbolic 3 -spaces.

Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues

Samuel Krushkal (2007)

Open Mathematics

The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to ^ are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = z: |z| > 1 can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely,...

Currently displaying 1 – 12 of 12

Page 1