Free boundary regularity for harmonic measures and Poisson kernels

One of the basic aims of this paper is to study the relationship between the geometry of ``hypersurface like'' subsets of Euclidean space and the properties of the measures they support. In this context we show that certain doubling properties of a measure determine the geometry of its support. A Radon measure is said to be doubling with constant C if C times the measure of the ball of radius r centered on the support is greater than the measure of the ball of radius 2r and the same center. We prove that if the doubling constant of a measure on \R^{n+1} is close to the doubling constant of the n-dimensional Lebesgue measure then its support is well approximated by n-dimensional affine spaces, provided that the support is relatively flat to start with. Primarily we consider sets which are boundaries of domains in \R^{n+1}. The n-dimensional Hausdorff measure may not be defined on the boundary of a domain in R^{n+1}. Thus we turn our attention to the harmonic measure which is well behaved under minor assumptions. We obtain a new characterization of locally flat domains in terms of the doubling properties of their harmonic measure. Along these lines we investigate how the ``weak'' regularity of the Poisson kernel of a domain determines the geometry of its boundary.Comment: 85 pages, published version, abstract added in migratio

Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions

In this work we introduce the use of powerful tools from geometric measure theory (GMT) to study problems related to the size and structure of sets of mutual absolute continuity for the harmonic measure $\omega^+$ of a domain $\Omega=\Omega^+\subset\mathbb{R}^n$ and the harmonic measure $\omega^-$ of $\Omega^-$, $\Omega^-=$int$(\Omega^c)$, in dimension $n\ge 3$

Repositorio visual de memorias: una alternativa tecnológica para ver y entender el conflicto en Colombia

Through the construction of a digital repository capable of containing the visual memories that have occurred in Colombia related to conflict and human rights violations, this article, which is derived from the research project Atlas Visual de la Memoria: Digital Repository of Memories (second phase), from the Memory and Society line of the Research Group on Information, Knowledge and Society of the University of Antioquia - Colombia, seeks to investigate alternative forms of knowledge representation and the construction of technological aids that To advance in the understanding of social problems

Socialist governmentality: political formation, revolutionary instruction, and socialist emulation in the CDR, Cuba, 1961-1965

During the 1960s, the Committees for the Defense of the Revolution (Comités de Defensa de la Revolución [CDR]) took relevant actions along with the Cuban masses, organizing cultural, social, and economic activities that shaped socialism from below. Thereby, through their work, the CDR gave meaning to their own idea of Cuban socialism. In the context of revolutionary upheaval, they were major players in the process of governmentality deployed by the revolutionary project. They willingly participated in their own governance. As a result, the CDR deployed a productive power that actually aimed at improving the lives of fellow Cubans. This article highlights the political formation of CDR members through revolutionary instruction and ideological formation. Also, this is an analysis of the role of CDR members in the revolutionary process beyond political surveillance, focusing on their impact in the everyday lives of Cuban people. The work of the CDR was key to build a new hegemonic project in revolutionary Cuba. They took a significant ideological role, creating and promoting a new cultural hegemony that sought to convince fellow Cubans about the potential benefits that the revolution could eventually bring. Thus, through the work of the CDR, we may see the Cuban Revolution beyond the vanguard.Keywords: Governmentality. Ideology. Socialist Emulation. Representations. Political Formation

Memoria, resistencia y empoderamiento social femenino por la vida y la dignidad.: El proceso de transformación del dolor de las madres de Soacha en los casos de los falsos positivos

The "false positives" scandal known as extrajudicial killings of thousands of civilians by the military forces has been one of the chapter most painfulness in the Colombian conflict. According with the JEP, 6402 civilians, were systematically executed beetween 2002 and 2010 whose bodies were then passed off as rebels to present them as combat kills. This situation erupted in 2008 when a group of poor young men had been recruited from the slum of Soacha (Cundinamarca) promised well-paying jobs in Norte de Santander were afterwards murdered. The victims, who were civilians outside the conflict and the illegal armed actors, were buried in mass graves, far from their places of origin and their families. The mobilization of their mothers to find their sons was not easy and only their love, resistance and their struggle for memory have allowed to know the truth, struggle because society knows what happened, demanding justice and guarantees of non-repetition.El escándalo de "falsos positivos" conocido como asesinatos extrajudiciales de miles de civiles por parte de las fuerzas militares ha sido uno de los capítulos más dolorosos en el conflicto colombiano. Según la JEP, 6402 civiles fueron ejecutados sistemáticamente entre 2002 y 2010, cuyos cuerpos fueron pasados a los guerrilleros para presentarlos como asesinatos de combate. Esta situación estalló y se hizo visible en 2008 cuando un grupo de jóvenes reclutados en los barrios periféricos de Soacha (Cundinamarca) fueron engañados y posteriormente asesinados a sangre fría.Las víctimas, quienes eran civiles ajenos al conflicto y los actores armados ilegales, fueron enterradas en fosas comunes, lejos de sus lugares de origen y sus familias. La movilización de sus madres para encontrar a sus hijos no fue fácil y solo su amor, resistencia y su lucha por la memoria han permitido conocer la verdad, luchar porque la sociedad conozca lo sucedido, exigir justicia y garantías de no repetición