Structure theorems for singular minimal laminations

Structure Theorems for o-Minimal Expansions of Groups

In this study the structure for O-minimal expansions of groups is considered Let be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) is semibounded, (2) has no poles, (3) cannot define a real closed field with domain R and order <, (4) is eventually linear and (5) every –definable set is a finit u...

Class of Limit Theorems for Singular Diffusions

Continuity of the Peierls Barrier and Robustness of Minimal Laminations

This chapter deals with finite range monotone variational recurrence relationsover Z. Such recurrence relations arise in solid state physics, conservative lattice dynamics and as Hamiltonian twist maps. An example is the Frenkel-Kontorova lattice. AubryMather theory guarantees the existence of action-minimizing solutions of every rotation number ω ∈ R. For every ω these minimizers form ordered ...

O-minimal Preparation Theorems

Macintyre, Marker and Van den Dries [6] use model theory to show that globally subanalytic functions are piecewise given by terms in a certain language. Adding symbols for the exponential and logarithm function to this language, they also show that functions definable from exponentiation and globally subanalytic functions are piecewise given by terms. This piecewise definability by terms inspir...

Some Structure Theorems for