[CvGmt News] CVGMT weekly bulletin

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Fri May 11 12:00:02 CEST 2012


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

--- Summary ---

* Seminars by: Marchese
* New papers by: Goldman, Carriero, Chambolle, Leaci, Novaga, Tomarelli
* Modified papers by: Goldman, Carriero, Leaci, Laptev, Sigalotti, Maggi, Kovarik, Rajala, Chambolle, Alicandro, De Philippis, Cicalese, Figalli, Novaga, Caffarelli, Tomarelli, Leonardi

--- Seminars next week ---

* Wednesday 16 may 2012
time: 17:00
Sala Seminari, Department of Mathematics, Pisa University

Rademacher's theorem for Euclidean measures
Andrea Marchese (Dip. Mat. Univ. Pisa)

Abstract. For every Euclidean Radon measure $\mu$ we state an adapted version of Rademacher's theorem, which is, in a certain sense, the best possible for the measure $\mu$. We define a sort of fibre bundle (actually a map $S$ that at each point $x\in\mathbb{R}^n$ associates a vector subspace $S(x)$ of $T_x\mathbb{R}^n$, possibly with non-costant dimension $k(x)$) such that every Lipschitz function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ is differentiable at $x$, along $S(x)$, for $\mu$-a.e. $x$. We prove that $S$ is maximal in the following sense: there exists a Lipschitz function $g:\mathbb{R}^n\rightarrow\mathbb{R}$ which doesn't admit derivative at $\mu$-a.e. $x$, along any direction not belonging to $S(x)$. Joint work with Giovanni Alberti.

--- New Papers ---

* Chambolle, Goldman, Novaga: Plane-like minimizers and differentiability of the stable norm

* Carriero, Leaci, Tomarelli: Free gradient discontinuity and image segmentation

--- Modified Papers ---

* Carriero, Leaci, Tomarelli: Free Gradient Discontinuity and Image Inpainting

* Kovarik: Eigenvalue asymptotic of Robin Laplace operators on two-dimensional domains with cusps

* Carriero, Leaci, Tomarelli: Euler Equations for  Blake & Zisserman Functional

* Kovarik, Laptev: Hardy inequalities for Robin Laplacians

* Carriero, Leaci, Tomarelli: Uniform Density Estimates for Blake & Zisserman Functional

* Rajala: Local Poincaré inequalities from stable curvature conditions on metric spaces

* Carriero, Leaci, Tomarelli: About Poincaré Inequalities for Functions Lacking Summability

* Caffarelli, Figalli: Regularity of solutions to the parabolic fractional obstacle problem

* Alicandro, Cicalese, Sigalotti: Phase transition in presence of surfactants: from discrete to continuum

* Kovarik: Heat kernels of two-dimensional magnetic Schrödinger and Pauli operators 

* Carriero, Leaci, Tomarelli: A candidate local minimizer of Blake & Zisserman functional

* Chambolle, Goldman, Novaga: Representation, relaxation and convexity for variational problems in Wiener spaces

* Cicalese, Leonardi: A Selection Principle for the Sharp Quantitative Isoperimetric Inequality

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

* De Philippis, Maggi: Sharp stability inequalities for the Plateau problem



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