[CvGmt News] CVGMT weekly bulletin

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--- Summary ---

* Seminars by: Marchi
* New papers by: Ambrosio, Almeida, Chambolle, Novaga, Fusco, Julin, Ambrosio, Rajala, Brasco, De Philippis, Ruffini, De Philippis, Figalli, Chambolle, Lemenant, Rajala
* Modified papers by: Pacini, Braides, Defranceschi, Vitali, Di Nezza, Palatucci, Valdinoci

--- Seminars next week ---

* Wednesday 30 nov 2011
time: 17:00
Sala Seminari, Department of Mathematics, Pisa University

Rectifiability of Sets of Finite Perimeter in a class of Carnot Groups of arbitrary step
Marco Marchi 

Abstract. In 1955, De Giorgi proved his well-known rectifiability theorem, combining the theory of perimeters of Caccioppoli with the theory of rectifiable sets. More recently, the same problem has been studied in more general settings and in particular in Carnot groups. In 2003 Franchi, Serapioni and Serra Cassano extended De Giorgi’s theorem to step 2 Carnot groups by using a blow-up technique. In 2009 Ambrosio, Kleiner and Le Donne achieved a partial result of blow-up, valid for any Carnot group, but today there are no general rectifiability results. In the seminar, I will show the main result of my master’s degree thesis: the existence of an algebric condition on the Lie algebra of a Carnot group that allows to extend Franchi, Serapioni and Serra Cassano’s results to a large class of Carnot groups of arbitrary step. In my thesis, such groups are called groups of type ⋆. Their stratified Lie algebra has the following property: there exists a basis (X1,...,Xm) of the first layer such that [Xj,[Xj,Xi]] = 0 for i,j = 1,...,m. Besides step 2 groups, the Lie groups of unit upper triangular matrices, which appear in the Iwasawa decomposition of the linear group, are examples of groups of type ⋆.


--- New Papers ---

* Ambrosio: An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below

* Almeida, Chambolle, Novaga: Mean curvature flow with obstacles

* Fusco, Julin: A strong form of the quantitative isoperimetric inequality

* Ambrosio, Rajala: Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces

* Brasco, De Philippis, Ruffini: Spectral optimization for the Stekloff--Laplacian: the stability issue

* De Philippis, Figalli: $W^{2,1}$ regularity for solutions of the Monge-Ampère equation

* Chambolle, Lemenant: The stress intensity factor for non-smooth fractures in antiplane elasticity

* Rajala: Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm

--- Modified Papers ---

* Pacini: Special Lagrangian conifolds, II: Gluing constructions in C^m

* Braides, Defranceschi, Vitali: A compactness result for a second-order variational discrete model

* Di Nezza, Palatucci, Valdinoci: Hitchhiker's guide to the fractional Sobolev spaces