Flexible Weinstein manifolds

This survey on flexible Weinstein manifolds is, essentially, an extract from our recent joint book.Comment: 41 pages, 8 figure

Stein structures: existence and flexibility

This survey on the topology of Stein manifolds is an extract from our recent joint book. It is compiled from two short lecture series given by the first author in 2012 at the Institute for Advanced Study, Princeton, and the Alfred Renyi Institute of Mathematics, Budapest.Comment: 29 pages, 11 figure

The topology of rationally and polynomially convex domains

We give in this article necessary and sufficient conditions on the topology of rationally and polynomially convex domains.Comment: 23 pages, no figures, final version to appear in Invent. Mat

Lagrangian caps

We establish an $h$-principle for exact Lagrangian embeddings with concave Legendrian boundary. We prove, in particular, that in the complement of the unit ball $B$ in the standard symplectic $\R^{2n}, 2n\geq 6$, there exists an embedded Lagrangian $n$-disc transversely attached to $B$ along its Legendrian boundary.Comment: 38 pages, 6 figure