Regularity via Minors and Applications to Conformal Maps

Regularity of optimal transport maps and applications

Combinatorically Prescribed Packings and Applications to Conformal and Quasiconformal Maps

The Andreev-Thurston Circle Packing Theorem is generalized to packings of convex bodies in planar simply connected domains. This turns out to be a useful tool for constructing conformal and quasiconformal mappings with interesting geometric properties. We attempt to illustrate this with a few results about uniformizations of finitely connected planar domains. For example, the following variatio...

Conformal Maps to Multiply Slit Domains and Applications

By exploiting conformal maps to vertically slit regions in the complex plane, a recently developed rational spectral method [27] is able to solve PDEs with interior layer-like behaviour using significantly fewer collocation points than traditional spectral methods. The conformal maps are chosen to ‘enlarge the region of analyticity’ in the solution: an idea which can be extended to other numeri...

Arens regularity of bilinear maps and Banach modules actions

‎Let $X$‎, ‎$Y$ and $Z$ be Banach spaces and $f:Xtimes Y‎ ‎longrightarrow Z$ a bounded bilinear map‎. ‎In this paper we‎ ‎study the relation between Arens regularity of $f$ and the‎ ‎reflexivity of $Y$‎. ‎We also give some conditions under which the‎ ‎Arens regularity of a Banach algebra $A$ implies the Arens‎ ‎regularity of certain Banach right module action of $A$‎ .

Large Deformation Registration via n-dimensional Quasi-conformal Maps

We propose a new method to obtain registration between n-dimensional manifolds with very large deformations. Given a set of landmark correspondences, our algorithm produces an optimal diffeomorphism that matches prescribed landmark constraints. The obtained registration is a n-dimensional quasi-conformal map. The basic idea of the model is to minimize an energy functional with a conformality te...