Alessandro Carlotto

Localizing solutions of the Einstein constraint equations

We perform an optimal localization of asymptotically flat initial data sets and construct data that have positive ADM mass but are exactly trivial outside a cone of arbitrarily small aperture. The gluing scheme that we develop allows to produce a new class of N-body solutions for the Einstein equation, which patently exhibit the phenomenon of gravitational shielding: for any large T we can engineer solutions where any two massive bodies do not interact at all for any time

Index estimates for free boundary minimal hypersurfaces

t\in (0,T)

Rigidity of Stable Marginally Outer Trapped Surfaces in Initial Data Sets

t∈(0,T), in striking contrast with the Newtonian gravity scenario.

Slowly converging Yamabe flows

In the first part of this article, we complete the program announced in the preliminary note [8] by proving a conjecture presented in [9] that states the equivalence of contractibility and p_{1}-stability for generalized spaces of formal barycenters and hence we get purely algebraic conditions for the solvability of the singular Liouville equation on Riemann surfaces. This relies on a structure decomposition theorem for these model spaces in terms of maximal strata, and on elementary combinatorial arguments based on the selection rules that define such spaces. Moreover, we also show that these solvability conditions on the parameters are not only sufficient, but also necessary at least when for some

Existence of Generalized Totally Umbilic 2-Spheres in Perturbed 3-Spheres

i\in{1,...,m}

A non-existence result for minimal catenoids in asymptotically flat spaces

the value

Weighted barycentric sets and singular Liouville equations on compact surfaces

\alpha_{i}

Rigidity of stable minimal hypersurfaces in asymptotically flat spaces

approaches -1. This disproves a conjecture made in Section 3 of [19] and gives the first non-existence result for this class of PDEs without any genus restriction. The argument we present is based on a combined use of maximum/comparison principle and of a Pohozaev type identity and applies for arbitrary choice both of the underlying metric g of