1. CJM 2013 (vol 65 pp. 1384)
 Wright, Paul

Estimates of Hausdorff Dimension for Nonwandering Sets of Higher Dimensional Open Billiards
This article concerns a class of open billiards consisting of a finite
number of strictly convex, noneclipsing obstacles $K$. The
nonwandering set $M_0$ of the billiard ball map is a topological
Cantor set and its Hausdorff dimension has been previously estimated
for billiards in $\mathbb{R}^2$, using wellknown techniques. We
extend these estimates to billiards in $\mathbb{R}^n$, and make
various refinements to the estimates. These refinements also allow
improvements to other results. We also show that in many cases, the
nonwandering set is confined to a particular subset of $\mathbb{R}^n$
formed by the convex hull of points determined by period 2
orbits. This allows more accurate bounds on the constants used in
estimating Hausdorff dimension.
Keywords:dynamical systems, billiards, dimension, Hausdorff Categories:37D20, 37D40 

2. CJM 2011 (vol 64 pp. 1058)
 Plakhov, Alexander

Optimal Roughening of Convex Bodies
A body moves in a rarefied medium composed of point particles at
rest. The particles make elastic reflections when colliding with the
body surface, and do not interact with each other. We consider a
generalization of Newton's minimal resistance problem: given two
bounded convex bodies $C_1$ and $C_2$ such that $C_1 \subset C_2
\subset \mathbb{R}^3$ and $\partial C_1 \cap \partial C_2 = \emptyset$, minimize the
resistance in the class of connected bodies $B$ such that $C_1 \subset
B \subset C_2$. We prove that the infimum of resistance is zero; that
is, there exist "almost perfectly streamlined" bodies.
Keywords:billiards, shape optimization, problems of minimal resistance, Newtonian aerodynamics, rough surface Categories:37D50, 49Q10 
