Nash functions on noncompact Nash manifolds

Nash Manifolds and Schwartz Functions on Them

These are the lecture notes for my talk on December 1, 2014 at the BIRS workshop “Motivic Integration, Orbital Integrals, and Zeta-Functions”. 1. Semi-algebraic sets and the Seidenberg-Tarski theorem In this section we follow [BCR]. Definition 1.1. A subset A ⊂ R is called a semi-algebraic set if it can be presented as a finite union of sets defined by a finite number of polynomial equalities a...

Global Problems on Nash Functions

This is a survey on the history of and the solutions to the basic global problems on Nash functions, which have been only recently solved, namely: separation, extension, global equations, Artin-Mazur description and idempotency, also noetherianness. We discuss all of them in the various possible contexts, from manifolds over the reals to real spectra of arbitrary commutative rings. Nash functio...

Nash-stampacchia Equilibrium Points on Manifolds

Motivated by Nash equilibrium problems on ’curved’ strategy sets, the concept of Nash-Stampacchia equilibrium points is introduced for a finite family of non-smooth functions defined on geodesic convex sets of certain Riemannian manifolds. Characterization, existence, and stability of NashStampacchia equilibria are studied when the strategy sets are compact/noncompact subsets of certain Hadamar...

A Note on Exponentially Nash G Manifolds and Vector Bundles

Global Structures on CR Manifolds via Nash Blow-ups

A generic compact real codimension two submanifold X of Cn+2 will have a CR structure at all but a finite number of points (failing at the complex jump points J). The main theorem of this paper gives a method of extending the CR structure on the non-jump points X − J to the jump points. We examine a Gauss map from X − J to an appropriate flag manifold F and take the closure of the graph of this...