Erratum to: Instantons from blow-up

Transition from decay to blow-up in a parabolic system

We show a locally uniform bound for global nonnegative solutions of the system ut = ∆u + uv − bu, vt = ∆v + au in (0, +∞) × Ω, u = v = 0 on (0, +∞)×∂Ω, where a > 0, b ≥ 0 and Ω is a bounded domain in R n , n ≤ 2. In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

From blow-up boundary solutions to equations with singular nonlinearities

In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane-Emden-Fowler equations with singu...

Summing up D-Instantons

We investigate quantum corrections to the moduli space for hypermultiplets for type IIA near a conifold singularity. We find a unique quantum deformation based on symmetry arguments which is consistent with a recent conjecture. The correction can be interpreted as an infinite sum coming from multiple wrappings of the Euclidean D-branes around the vanishing cycle.

How to blow up a massive star

Summing up Dirichlet Instantons.

We investigate quantum corrections to the moduli space for hypermultiplets for the type IIA string near a conifold singularity. We find a unique quantum deformation based on symmetry arguments which is consistent with a recent conjecture. The correction can be interpreted as an infinite sum coming from multiple wrappings of the Euclidean Dirichlet branes around the vanishing cycle. [S0031-9007(...