[CvGmt News] CVGMT: weekly bulletin

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Subject: CVGMT weekly bulletin

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

--- Summary ---

* Seminars by: Parini
* New papers by: Georgiev, Goldman, Chambolle, Novaga, Boscain, Maggi, Jendrej, Agrachev, Focardi, Cicalese, Mucci, Stepanov, Barilari, Acerbi, Leonardi
* Modified papers by: Nicolodi, Brasco, Mantegazza, Rimoldi, Freddi, Petrache, Paroni, De Faveri, Focardi, Mucci, Mongodi, De Lellis, Stepanov, Paolini

--- News --- 

* Join the Encyclopedia of Mathematics!: The [Encyclopedia of Mathematics|http://www.encyclopediaofmath.org/index.php/Main_Page] wiki is an open access resource designed specifically for the mathematics community. The original articles are from the online Enyclopedia of Mathematics, published by Kluwer Academic Publishers in 2002. With more than 8.000 entries, illuminating nearly 50.000 notions in mathematics, the Encyclopedia of Mathematics was the most up-to-date graduate-level reference work in the field of mathematics.


Springer, in cooperation with the European mathematical society, has made the content of this Encyclopedia freely open to the public. The original articles go back to the Soviet Matematicheskaya entsiklopedya (1977), originally edited by Ivan Matveevich Vinogradov. The electronic version had its formulae written in TEX, but its code was lost: most of the current pages have the formulas saved as png images.

Though starting from a wealth of material, written by professional mathematicians there is a lot to do! From the routine task of retyping old pages in Tex to the one of updating the contents and correcting mistakes; from adding to the pages nice new media (pictures and videos) to creating completely new entries encompassing the last exciting developments of math. Whether you are an undergraduate student, a graduate student or a professional mathematician you are welcome to join us in this project. Unlike other wikis, there is an [editorial board|http://www.encyclopediaofmath.org/index.php/Editorial_Board] monitoring the various pages, but just like other wikis anybody who makes a user account is free to discuss and modify things. It is also very easy to use: if you know Tex you will be able to write new pages in a few minutes. At [this web page|http://www.encyclopediaofmath.org/index.php/User:Camillo.delellis] you will find my contributions to the Encyclopedia.

*Join us!*

But of course, even if you do not want to become a contributor, just give it sometimes a try if you are looking for quick explanations, definitions, history or references: I am confident you will find out it is a great tool to learn math.


--- Seminars next week ---

* Tuesday 13 nov 2012
time: 17:00
Sala Seminari, Department of Mathematics, Pisa University

Optimal constants for higher-order functional embeddings
Enea Parini 

Abstract. We consider the problem of finding the optimal constant for the embedding of the space \[ W^{2,1}_\Delta(\Omega) := \left\{ u \in W^{1,1}_0(\Omega)\,|\,\Delta u \in L^1(\Omega)\right\} \] into the space $L^1(\Omega)$, where $\Omega\subset \mathbb R^n$ is a bounded, convex domain, or a bounded domain with boundary of class $C^{1,\alpha}$. This is equivalent to find the first eigenvalue of the 1-biharmonic operator under (generalized)  Navier boundary conditions. In this talk we provide an interpretation for the eigenvalue problem, we show some properties of the first eigenfunction, we prove an inequality of Faber-Krahn type, and we compute the first eigenvalue and the associated eigenfunction explicitly for a ball, and in terms of the torsion function for general domains. We will also state some results about the embedding into $L^1(\Omega)$ of the subspace $W^{2,1}_{\Delta,0}(\Omega)$, consisting of those functions of $W^{2,1}_\Delta(\Omega)$ obtained as limits of sequences of smooth functions with compact support.

--- New Papers ---

* Georgiev, Stepanov: Metric cycles, curves and solenoids

* Cicalese, Leonardi, Maggi: Sharp stability inequalities for planar double bubbles

* Focardi: $\Gamma$-convergence: a tool to investigate physical phenomena across scales 

* Acerbi, Mucci: Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation

* Chambolle, Goldman, Novaga: Existence and qualitative properties of isoperimetric sets in periodic media

* Barilari, Jendrej: Small time heat kernel asymptotics at the cut locus on two-spheres of revolution

* Agrachev, Barilari, Boscain: Introduction to Riemannian and Sub-Riemannian geometry

--- Modified Papers ---

* Mucci, Nicolodi: On the elastic energy density of constrained $Q$-tensor models for biaxial nematics

* Focardi: Vector-valued obstacle problems for non-local energies

* De Lellis, Focardi: Higher integrability of the gradient for minimizers of the 2d Mumford-Shah energy 

* Mantegazza, Mongodi, Rimoldi: The Cotton tensor and the Ricci flow

* De Lellis, Focardi: Density lower bound estimates for local minimizers of the 2d Mumford-Shah energy

* De Faveri, Freddi, Paroni: No-tension bodies: a reinforcement problem

* Paolini, Stepanov: Structure of metric cycles and normal one-dimensional currents

* Brasco, Petrache: A continuous model of transportation revisited

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