[CvGmt News] [CVGMT] weekly bulletin

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Fri Feb 6 12:00:02 CET 2015

Weekly bulletin of http://cvgmt.sns.it

--- Summary ---
* Seminars by: Carlotto, Carlotto
* New papers by: Lazzaroni, Crismale, Bouchitté, Buttazzo* Modified papers by: Lazzaroni, Carlotto, Massaccesi, Ambrosio, Van Schaftingen, Spector, Kovarik, Zeppieri, Schikorra, Barchiesi, Paolini, Weidl, Ritoré, Teplitskaya, De Lellis, Galli, Stepanov, Schmidt
--- Seminars next week ---
* Wednesday 11 feb 2015

time: 17:30
Dipartimento di Matematica, Aula seminari
Variations on the Bernstein problem in asymptotically flat spaces
Alessandro Carlotto 
Abstract. The Bernstein problem, namely the problem of classifying all entire minimal hypergraphs in Euclidean spaces has played a crucial role in the development of Analysis throughout the whole course of the twentieth century. In this talk, I will discuss its natural extension to asymptotically flat manifolds, where it is motivated by the study of the large-scale structure of initial data sets for the Einstein field equation. I will first present the basic non-existence result and its relation to the asymptotic Plateau problem and then mention the application of similar techniques to the study of 
1) large CMC spheres and isoperimetric domains (C.-Chodosh-Eichmair), 
2) marginally outer-trapped surfaces (C.) and 3) the zero set of static potentials (Galloway-Miao). 

* Friday 13 feb 2015

time: 14:30
Scuola Normale, Aula Bianchi
Localizing solutions of the Einstein constraint equations
Alessandro Carlotto 
Abstract. A well-known corollary of the positive mass theorem by Schoen-Yau is that if an asymptotically flat manifold (of non-negative scalar curvature) is exactly flat outside of a compact set, then it has to be globally flat: in other terms any such metric can never be localized inside a compact set. So what is the "optimal" localization of those metrics? For instance, can one produce scalar non-negative metrics that have positive ADM mass and still are trivial in a half-space? 

In recent joint work with Schoen, we answer these questions by giving a systematic method for constructing solutions to the Einstein constraint equations that are localized inside a cone of arbitrarily small aperture. This sharply contrasts with various recent scalar curvature rigidity phenomena both in the closed and in the free-boundary setting. Moreover, the gluing scheme that we adopt allows to produce a new class of exotic 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 t\in(0,T), in striking contrast with the Newtonian gravity scenario.

--- New Papers ---
* Crismale, Lazzaroni: Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model
* Bouchitté, Buttazzo: Optimal design problems for Schrödinger operators with noncompact resolvents
--- Modified Papers ---
* Ambrosio, Carlotto, Massaccesi: Lecture Notes on Partial Differential Equations
* Schikorra, Spector, Van Schaftingen: An $L^1$-type estimate for Riesz potentials
* Ambrosio, De Lellis, Schmidt: Partial regularity for mass-minimizing currents in Hilbert spaces
* Paolini, Stepanov, Teplitskaya: An example of an infinite Steiner tree connecting an uncountable set
* Kovarik: On the lowest eigenvalue of Laplace operators with mixed boundary conditions
* Kovarik, Weidl: Improved Berezin-Li-Yau inequalities with magnetic field
* Barchiesi, Lazzaroni, Zeppieri: A bridging mechanism in the homogenisation of brittle composites with soft inclusions
* Galli, Ritoré: Regularity of $C^1$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds
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