Regularity of continuous CR maps in arbitrary dimension

Cellular Modeling in Arbitrary Dimension using Generalized Maps

Combinatorial topology is a recent field of mathematics which promises to be of great benefit to geometric modeling and CAD. As such, this article shows how the notion of Generalized Map (GMap) can be used to implement a dimension-independent topological kernel for industrial scale modelers and partial derivative equation (PDE) solvers. Classic approaches to this issue either require a large nu...

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 $A$‎ .

Regularity of Harmonic Maps

Global Regularity of Wave Maps I. Small Critical Sobolev Norm in High Dimension

We show that wave maps from Minkowski space R to a sphere Sm−1 are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space Ḣn/2, in the high-dimensional case n ≥ 5. A major difficulty, not present in earlier results in this area, is that the Ḣn/2 norm barely fails to control L, potentially causing a logarithmic divergence in the non-linearity; however this...

Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds

If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of  graph(f) is as big as possible and the lower box dimension of graph(f) is as small as possible.