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<h1>CVGMT Weekly Bulletin</h1>
<h2>Summary</h2>
<p><b>Seminars by:</b> <a href='/seminar/453/'>Carlotto</a></p>
<p><b>New papers by:</b> <a href='/person/58/' >De Lellis</a>, <a href='/person/1644/' >Almi</a>, <a href='/person/245/' >Focardi</a></p>
<p><b>Modified papers by:</b> <a href='/person/3/'>Ambrosio</a>, <a >Milakis</a>, <a href='/person/263/'>Mantegazza</a>, <a >Chambolle</a>, <a href='/person/12/'>Bardi</a>, <a href='/person/22/'>De Philippis</a>, <a >Spinolo</a>, <a href='/person/260/'>Goldman</a>, <a >Álvarez-Caudevilla</a>, <a href='/person/544/'>Cesaroni</a>, <a href='/person/164/'>Mazzieri</a>, <a >Bonnivard</a>, <a href='/person/135/'>Catino</a>, <a >Valdinoci</a>, <a >Parini</a>, <a href='/person/198/'>Brasco</a>, <a href='/person/201/'>Santambrogio</a>, <a href='/person/973/'>Ruffini</a>, <a href='/person/1753/'>De Rosa</a>, <a href='/person/90/'>Ghiraldin</a>, <a >Carlotto</a>, <a href='/person/866/'>Massaccesi</a>, <a >Royer-carfagni</a>, <a >Scotti</a>, <a href='/person/119/'>Novaga</a>, <a href='/person/250/'>Lemenant</a></p>
<p><b>Open positions:</b> <a href='/position/131/'>PhD position in Applied Analysis at the University of Bath</a>; <a href='/position/135/'>Postdoc Position in Münster</a>; <a href='/position/137/'>Postdoc Positions in Jyväskylä</a></p>
<h2>Seminars next week</h2>
<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> De Lellis, Focardi:</b> <a href='/paper/2622/'>Endpoint regularity of $2$d Mumford-Shah minimizers</a></p>
<p><b> Almi:</b> <a href='/paper/2623/'>Energy release rate and quasi-static evolution via vanishing viscosity in a cohesive fracture model with an activation threshold</a></p>
<h2>Modified Papers</h2>
<p><b> Álvarez-Caudevilla, Lemenant:</b> <a href='/paper/104/'>Asymptotic analysis for some linear eigenvalue problems via Gamma-Convergence</a></p>
<p><b> Ambrosio, Lemenant, Royer-carfagni:</b> <a href='/paper/723/'>A variational model for plastic slip and its regularization via Gamma-convergence.</a></p>
<p><b> Lemenant, Milakis:</b> <a href='/paper/837/'>Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in R^N</a></p>
<p><b> Lemenant, Milakis:</b> <a href='/paper/864/'>A stability result for nonlinear Neumann problems in Reifenberg flat domains in $\mathbb R^N$.</a></p>
<p><b> Ambrosio, Carlotto, Massaccesi:</b> <a href='/paper/1280/'>Lecture Notes on Partial Differential Equations</a></p>
<p><b> Lemenant:</b> <a href='/paper/1393/'>A presentation of the average distance minimizing problem</a></p>
<p><b> Lemenant:</b> <a href='/paper/1615/'>About the regularity of average distance minimizers in R^2</a></p>
<p><b> Chambolle, Lemenant:</b> <a href='/paper/1696/'>The stress intensity factor for non-smooth fractures in antiplane elasticity</a></p>
<p><b> Cesaroni, Novaga, Valdinoci:</b> <a href='/paper/1815/'>A symmetry result for the Ornstein-Uhlenbeck operator</a></p>
<p><b> Lemenant, Milakis, Spinolo:</b> <a href='/paper/1908/'>On the extension property of Reifenberg-flat domains</a></p>
<p><b> Lemenant, Milakis, Spinolo:</b> <a href='/paper/1909/'>Spectral Stability Estimates for the Dirichlet and Neumann Laplacian in rough domains</a></p>
<p><b> Catino, Mantegazza, Mazzieri:</b> <a href='/paper/2221/'>Locally Conformally Flat Ancient Ricci Flows</a></p>
<p><b> Goldman, Novaga, Ruffini:</b> <a href='/paper/2267/'>Existence and stability for a non-local isoperimetric model of charged liquid drops</a></p>
<p><b> Novaga, Ruffini:</b> <a href='/paper/2335/'>Brunn-Minkowski inequality for the $1$-Riesz capacity and level set convexity for the $1/2$-Laplacian</a></p>
<p><b> Bonnivard, Lemenant, Santambrogio:</b> <a href='/paper/2384/'>Approximation of length minimization problems among compact connected sets.</a></p>
<p><b> Lemenant:</b> <a href='/paper/2386/'>A rigidity result for global Mumford-Shah minimizers in dimension three</a></p>
<p><b> Bardi, Cesaroni, Scotti:</b> <a href='/paper/2442/'>Convergence in Multiscale Financial Models with Non-Gaussian Stochastic Volatility</a></p>
<p><b> Brasco, Parini:</b> <a href='/paper/2522/'>The second eigenvalue of the fractional $p-$Laplacian</a></p>
<p><b> De Philippis, De Rosa, Ghiraldin:</b> <a href='/paper/2615/'>A direct approach to Plateau's problem in any codimension</a></p>
<h2>Open Positions</h2>
<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>
<p> <a href="/position/137/">Postdoc Positions in Jyväskylä</a> (deadline: 31 Mar 2015) </p>
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