Lipschitz and quasiconformal approximation of homeomorphism pairs

Quasiconformal Lipschitz Maps, Sullivan's Convex Hull Theorem and Brennan's Conjecture

Winning sets, quasiconformal maps and Diophantine approximation

This paper describes two new types of winning sets in R, defined using variants of Schmidt’s game. These strong and absolute winning sets include many Diophantine sets of measure zero and first category, and have good behavior under countable intersections. Most notably, they are invariant under quasiconformal maps, while classical winning sets are not.

Quasiconformal Approximation by Eremenko-lyubich Functions

We discuss a method for constructing functions in the EremenkoLyubich class of transcendental functions with bounded singular set whose infinite tracts have prescribed geometry. Date: Nov 2011. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

Smooth Approximation of Lipschitz Projections

We show that any Lipschitz projection-valued function p on a connected closed Riemannian manifold can be approximated uniformly by smooth projection-valued functions q with Lipschitz constant close to that of p. This answers a question of Rieffel.

Non-Lipschitz Semi-Infinite Optimization Problems Involving Local Cone Approximation

In this paper we study the nonsmooth semi-infinite programming problem with inequality constraints. First, we consider the notions of local cone approximation $Lambda$ and $Lambda$-subdifferential. Then, we derive the Karush-Kuhn-Tucker optimality conditions under the Abadie and the Guignard constraint qualifications.