[CvGmt News] [CVGMT] weekly bulletin
web at cvgmt.sns.it
web at cvgmt.sns.it
Fri Feb 13 12:00:01 CET 2015
Weekly bulletin of http://cvgmt.sns.it
--- Summary ---
* Seminars by: Carlotto
* New papers by: De Lellis, Almi, Focardi* Modified papers by: Ambrosio, Milakis, Mantegazza, Chambolle, Bardi, De Philippis, Spinolo, Goldman, Álvarez-Caudevilla, Cesaroni, Mazzieri, Bonnivard, Catino, Valdinoci, Parini, Brasco, Santambrogio, Ruffini, De Rosa, Ghiraldin, Carlotto, Massaccesi, Royer-carfagni, Scotti, Novaga, Lemenant
--- Seminars next week ---
* Friday 13 feb 2015
Scuola Normale, Aula Bianchi
Localizing solutions of the Einstein constraint equations
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 ---
* De Lellis, Focardi: Endpoint regularity of $2$d Mumford-Shah minimizers
* Almi: Energy release rate and quasi-static evolution via vanishing viscosity in a cohesive fracture model with an activation threshold
--- Modified Papers ---
* Álvarez-Caudevilla, Lemenant: Asymptotic analysis for some linear eigenvalue problems via Gamma-Convergence
* Ambrosio, Lemenant, Royer-carfagni: A variational model for plastic slip and its regularization via Gamma-convergence.
* Lemenant, Milakis: Quantitative stability for the first Dirichlet eigenvalue in Reifenberg flat domains in R^N
* Lemenant, Milakis: A stability result for nonlinear Neumann problems in Reifenberg flat domains in $\mathbb R^N$.
* Ambrosio, Carlotto, Massaccesi: Lecture Notes on Partial Differential Equations
* Lemenant: A presentation of the average distance minimizing problem
* Lemenant: About the regularity of average distance minimizers in R^2
* Chambolle, Lemenant: The stress intensity factor for non-smooth fractures in antiplane elasticity
* Cesaroni, Novaga, Valdinoci: A symmetry result for the Ornstein-Uhlenbeck operator
* Lemenant, Milakis, Spinolo: On the extension property of Reifenberg-flat domains
* Lemenant, Milakis, Spinolo: Spectral Stability Estimates for the Dirichlet and Neumann Laplacian in rough domains
* Catino, Mantegazza, Mazzieri: Locally Conformally Flat Ancient Ricci Flows
* Goldman, Novaga, Ruffini: Existence and stability for a non-local isoperimetric model of charged liquid drops
* Novaga, Ruffini: Brunn-Minkowski inequality for the $1$-Riesz capacity and level set convexity for the $1/2$-Laplacian
* Bonnivard, Lemenant, Santambrogio: Approximation of length minimization problems among compact connected sets.
* Lemenant: A rigidity result for global Mumford-Shah minimizers in dimension three
* Bardi, Cesaroni, Scotti: Convergence in Multiscale Financial Models with Non-Gaussian Stochastic Volatility
* Brasco, Parini: The second eigenvalue of the fractional $p-$Laplacian
* De Philippis, De Rosa, Ghiraldin: A direct approach to Plateau's problem in any codimension
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