This is a short description of some results obtained by Ewa Damek, Andrzej Hulanicki, Richard Penney and Jacek Zienkiewicz. They belong to harmonic analysis on a class of solvable Lie groups called NA. We apply our results to analysis on classical Siegel domains.
We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in and to give a sufficient condition for the complete hyperbolicity of a domain in .
The states of the title are a set of knot types which suffice to create a generating set for the Kauffman bracket skein module of a manifold. The minimum number of states is a topological invariant, but quite difficult to compute. In this paper we show that a set of states determines a generating set for the ring of characters of the fundamental group, which in turn provides estimates of the invariant.
We study the class of smooth bounded weakly pseudoconvex domains D ⊂ ℂⁿ whose boundary points are of finite type (in the sense of J. Kohn) and whose Levi form has at most one degenerate eigenvalue at each boundary point, and prove effective estimates on the invariant distance of Carathéodory. This completes the author's investigations on invariant differential metrics of Carathéodory, Bergman, and Kobayashi in the corank one situation and on invariant distances on pseudoconvex finite type domains...
Using explicit integral formulas introduced by Skoda, we obtain Hölder estimates for the δ-equation in convex domains of finite type in C2.