[CvGmt News] CVGMT: weekly bulletin

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Fri Jan 25 12:00:02 CET 2013


Subject: CVGMT weekly bulletin

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

--- Summary ---

* Seminars by: Mondino
* New papers by: Goldman, Chambolle, Klein, Bellettini, Sparber, Ghiraldin, Markovich, Figalli
* Modified papers by: Gigli, Buttazzo, Santambrogio, Ruffini, Velichkov, Iurlano, Bonnotte

--- Seminars next week ---

* Wednesday 30 jan 2013
time: 17:00
Sala Seminari, Department of Mathematics, Pisa University

 A new notion of angle between three points in a metric space
Andrea Mondino (Scuola Normale Superiore (Pisa))

Abstract. We give a new notion of angle in general metric spaces; more precisely, given a triple of points p,x,q in a metric space (X,d), we introduce the notion of angle cone as being an interval defined in terms of the  distance functions from p and q via a duality construction  of differentials and gradients holding for locally Lipschitz functions on a general metric space. Our definition in the  Euclidean plane gives the standard angle between three points. We show that in general the angle cone is not single valued even in case the metric space is a smooth Riemannian manifold), but if we endow the metric space with a positive Borel measure m obtaining the metric measure space (X,d,m)then under quite general assumptions (which  include many fundamental examples as Riemannian manifolds, finite fimensional Alexandrov spaces with curvature bounded from below, Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below, and normed spaces with strictly convex norm), fixed p,q in X, the angle cone is single valued for m-a.e. x in X. We prove some basic  properties of the angle cone (such as the invariance under homotheties of the space) and we analyze in detail the case (X,d,m) is a measured-Gromov-Hausdorff limit of a sequence of Riemannian manifolds with Ricci curvature bounded from below, showing the consistency of our definition with a recent construction of Honda.

--- New Papers ---

* Bellettini, Chambolle, Goldman: The Gamma-limit  for singularly perturbed functionals of Perona-Malik type in arbitrary dimension

* Ghiraldin: Variational approximation of a functional of Mumford-Shah type in codimension higher than one

* Figalli, Klein, Markovich, Sparber: WKB analysis of Bohmian dynamics

--- Modified Papers ---

* Gigli: On the Heat flow on metric measure spaces: existence, uniqueness and stability

* Santambrogio: Flots de gradient dans les espaces m?triques et leurs applications (d'apr?s Ambrosio-Gigli-Savar?)

* Bonnotte: From Knothe's Rearrangement to Brenier's Optimal Transport Map

* Buttazzo, Ruffini, Velichkov: Shape Optimization Problems for Metric Graphs

* Iurlano: A density result for GSBD and its application to the approximation of brittle fracture energies

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