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<h1>CVGMT Weekly Bulletin</h1>
<h2>Summary</h2>
<p><b>Seminars by:</b> <a href='/seminar/451/'>Carlotto</a>, <a href='/seminar/453/'>Carlotto</a></p>
<p><b>New papers by:</b> <a href='/person/96/' >Lazzaroni</a>, <a href='/person/1642/' >Crismale</a>, <a href='/person/52/' >Bouchitté</a>, <a href='/person/262/' >Buttazzo</a></p>
<p><b>Modified papers by:</b> <a href='/person/96/'>Lazzaroni</a>, <a >Carlotto</a>, <a href='/person/866/'>Massaccesi</a>, <a href='/person/3/'>Ambrosio</a>, <a >Van Schaftingen</a>, <a href='/person/39/'>Spector</a>, <a href='/person/173/'>Kovarik</a>, <a href='/person/112/'>Zeppieri</a>, <a >Schikorra</a>, <a href='/person/116/'>Barchiesi</a>, <a href='/person/117/'>Paolini</a>, <a >Weidl</a>, <a >Ritoré</a>, <a href='/person/1401/'>Teplitskaya</a>, <a href='/person/58/'>De Lellis</a>, <a href='/person/1744/'>Galli</a>, <a href='/person/26/'>Stepanov</a>, <a href='/person/638/'>Schmidt</a></p>
<p><b>Open positions:</b> <a href='/position/136/'>Post doc position on Evolution Problems in Plasticity and Fracture</a>; <a href='/position/131/'>PhD position in Applied Analysis at the University of Bath</a>; <a href='/position/135/'>Postdoc Position in Münster</a></p>
<h2>Seminars next week</h2>
<p><i>Wednesday 11 feb 2015</i></p>
<p>
time: 17:30<br /> Dipartimento di Matematica, Aula seminari<br/>
<b><a href='/seminar/451/'>Variations on the Bernstein problem in asymptotically flat spaces</a></b><br />
Alessandro Carlotto <br />
<b>Abstract.</b> <p>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).
</p>
<br /> <p><i>Friday 13 feb 2015</i></p>
<p>
time: 14:30<br /> Scuola Normale, Aula Bianchi<br/>
<b><a href='/seminar/453/'>Localizing solutions of the Einstein constraint equations</a></b><br />
Alessandro Carlotto <br />
<b>Abstract.</b> <p>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?
</p>
<p>
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.</p>
<br />
<h2>New Papers</h2>
<p><b> Crismale, Lazzaroni:</b> <a href='/paper/2620/'>Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model</a></p>
<p><b> Bouchitté, Buttazzo:</b> <a href='/paper/2621/'>Optimal design problems for Schrödinger operators with noncompact resolvents</a></p>
<h2>Modified Papers</h2>
<p><b> Ambrosio, Carlotto, Massaccesi:</b> <a href='/paper/1280/'>Lecture Notes on Partial Differential Equations</a></p>
<p><b> Schikorra, Spector, Van Schaftingen:</b> <a href='/paper/2566/'>An $L^1$-type estimate for Riesz potentials</a></p>
<p><b> Ambrosio, De Lellis, Schmidt:</b> <a href='/paper/2112/'>Partial regularity for mass-minimizing currents in Hilbert spaces</a></p>
<p><b> Paolini, Stepanov, Teplitskaya:</b> <a href='/paper/2208/'>An example of an infinite Steiner tree connecting an uncountable set</a></p>
<p><b> Kovarik:</b> <a href='/paper/2320/'>On the lowest eigenvalue of Laplace operators with mixed boundary conditions</a></p>
<p><b> Kovarik, Weidl:</b> <a href='/paper/2321/'>Improved Berezin-Li-Yau inequalities with magnetic field</a></p>
<p><b> Barchiesi, Lazzaroni, Zeppieri:</b> <a href='/paper/2613/'>A bridging mechanism in the homogenisation of brittle composites with soft inclusions</a></p>
<p><b> Galli, Ritoré:</b> <a href='/paper/2616/'>Regularity of $C^1$ surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds</a></p>
<h2>Open Positions</h2>
<p> <a href="/position/136/">Post doc position on Evolution Problems in Plasticity and Fracture</a> (deadline: 6 Feb 2015) </p>
<p> <a href="/position/131/">PhD position in Applied Analysis at the University of Bath</a> (deadline: 13 Feb 2015) </p>
<p> <a href="/position/135/">Postdoc Position in Münster</a> (deadline: 31 Mar 2015) </p>
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