Finite unions of balls in C^n are rationally convex

It is shown that the rational convexity of any finite union of disjoint closed balls in C^n follows easily from the results of Duval and Sibony.Comment: V.2 - minor edits, 2 page

Uniformization of strictly pseudoconvex domains

It is shown that two strictly pseudoconvex Stein domains with real analytic boundaries have biholomorphic universal coverings provided that their boundaries are locally biholomorphically equivalent. This statement can be regarded as a higher dimensional analogue of the Riemann uniformization theorem

Legendrian links and d\'ej\`a vu moments

A Legendrian link is called a d\'ej\`a vu link if its components can be connected by a positive Legendrian isotopy but this isotopy cannot be embedded. This is the contact geometric analogue of a pair of events in a spacetime such that there are d\'ej\`a vu moments on every future-directed timelike path between them. We construct d\'ej\`a vu links in several geometrically relevant situations and discuss their basic properties.Comment: V.2 - small edits incorporating referee comments, references added; 20 pages, 4 figure