Let T be a Fourier integral operator on K" of order —(n — l)/2. Seeger, Sogge, and Stein showed (among other things) that T maps the Hardy space H to L. In this note we show that T is also of weak-type (1, 1). The main ideas are a decomposition of T into non-degenerate and degenerate components, and a factorization of the non-degenerate portion. 2000 Mathematics subject classification: primary ...

We find good dynamical compactifications for arbitrary polynomial mappings of C and use them to show that the degree growth sequence satisfies a linear integral recursion formula. For maps of low topological degree we prove that the Green function is well behaved. For maps of maximum topological degree, we give normal

Over the years the author has been interested in rigidity problems on bounded symmetric domains of rank ≥ 2. In this article we give an overview on rigidity problems arising from holomorphic mappings either on bounded symmetric domains of rank ≥ 2 or on their finite-volume quotient manifolds into complex manifolds, placing the focus on recent developments. The article highlights the use of some...

The original Novikov conjecture concerns the (oriented) homotopy invariance of higher signatures of manifolds and is equivalent to the rational injectivity of the assembly map in surgery theory. The integral injectivity of the assembly map is important for other purposes and is called the integral Novikov conjecture. There are also assembly maps in other theories and hence related Novikov and i...

Consider the Fulton-MacPherson configuration space of n points on P1, which is isomorphic to a certain moduli space of stable maps to P1. We compute the cone of effective Sn-invariant divisors on this space. This yields a geometric interpretation of known asymptotic formulas for the number of integral points of bounded height on compactifications of SL2 in the space of binary forms of degree n ...

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [5, 9], which give, respectively, the exact Kontsevich integral of the unknot and a map intertwining two natural products on a space of diagrams. It turns out that the Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on a wire), and its i...

Let (M,ω,Φ) be a Hamiltonian T -space and let H ⊆ T be a closed Lie subtorus. Under some technical hypotheses on the moment map Φ, we prove that there is no additive torsion in the integral full orbifoldK-theory of the orbifold symplectic quotient [M//H ]. Our main technical tool is an extension to the case of moment map level sets the well-known result that components of the moment map of a Ha...

In this paper, we study for some of the fixed point of mapping for a self map on a metric space under a contractive of integral type.

The purpose of this note is to announce two new theories of generalized differentials—the “generalized differential quotients,” abbr. GDQs, and the “path-integral generalized differentials”, abbr. PIGDs—which have good open mapping properties and lead to general versions of the maximum principle. In particular, we use GDQ theory to state—in Theorem 5— a version of the maximum principle for hybr...