The classification of complete stable area-stationary surfaces in the Heisenberg group H1\mathbb{H}^1

We prove that any $C^2$ complete, orientable, connected, stable area-stationary surface in the sub-Riemannian Heisenberg group $\mathbb{H}^1$ is either a Euclidean plane or congruent to the hyperbolic paraboloid $t=xy$.Comment: 32 pages, no figures, added reference missed in version

La moral pública y los jueces

Die vorliegende Arbeit untersucht die moralischen Grundlagen der Anwendung von Sanktionen gegenüber Verhaltensweisen welche die öffentliche Ordnung gefährden oder verletzen. Es wird die Rolle der Richter bei der Bewertung und Verurteilung dieser Akte unter dem Aspekt des Schadenprinzips untersucht.The current piece of work looks into the moral basis for suspension implementation for behavior against public order. We will thus study the role of judges to assess and judge such behavior, under the principle of damage.El presente trabajo analizará el fundamento moral para la aplicación de sanciones por las conductas que alteran y lesionan el orden público. Por lo que se estudiará el papel de los jueces al valorar y juzgar esos actos bajo el principio del daño

Design, health and circular economy.

Products generate waste in a linear value production model design. New sustainable design methods focus on using bio-materials and re-manufacturing processes to decrease waste and impact on the environment. Circular Economy models are sustainable because they aim to keep the value of a product at the end of their useful life. They reintegrate products in the chain instead of becoming waste and lose their value. However, circular models require an understanding of the big picture of business model ecosystems on what, who and how everyone closes the loop. Furthermore, the Internet of Things in product-service systems (PSS) requires the integration of diverse perspectives in their conception and design. The objective of this thesis is to find a way to create circular PSS concepts in circular economy models through a collaborative design approach. The approach extracts the expertise of other areas to understand the real needs of all stakeholders to close the gap between design and business perspectives. It aims to understand what value means for each stakeholder, the implications of moving towards circular economy models, the impact on the product architecture, the technological trends opportunities and the experiences that the users and customers desire. The study case for the thesis focuses on chronic diseases in Finland, especially for ischemic heart diseases which are the leading cause of deaths triggered by a cardiac arrest. The cardiopulmonary resuscitation (CPR), and the automated external defibrillator (AED) are fundamental to save a life. Methods, tools and principles of PSS and circular models, combined with Human-Centred Design (HCD) approaches, identify a problem space and possible solutions for circularity and usability in the study case. The limits of this research are that the time scope for the project only reached the design concept stage, without the implications of standards for medical equipment for a future product development stage. The outcomes of the research are insights for CPR and AED as a product-service system in circular economy models. However, the principal value is a new canvas that analyses a product -from the perspectives of design, business and technology- to map all the implications required to transform a product into a PSS in a circular model; integrating experts in a collaborative workshop to validate the model. The complexity of product-service systems in circular models resides in their natural transdisciplinarity. The number of stakeholders and their expertise surpass the knowledge of design to understand their processes. Alongside the contribution of the new canvas, the main conclusion for this work is that transdisciplinary projects could be led through the collaborative design approach under two conditions. The first condition is when the designer understands the meanings of concepts across disciplines, and secondly when the project has access to all the critical stakeholders in the project’s ecosystem. Thus, the need for transdisciplinary tools for design approaches requires further analysis and development

The last five years of Big Data Research in Economics, Econometrics and Finance: Identification and conceptual analysis

Today, the Big Data term has a multidimensional approach where five main characteristics stand out: volume, velocity, veracity, value and variety. It has changed from being an emerging theme to a growing research area. In this respect, this study analyses the literature on Big Data in the Economics, Econometrics and Finance field. To do that, 1.034 publications from 2015 to 2019 were evaluated using SciMAT as a bibliometric and network analysis software. SciMAT offers a complete approach of the field and evaluates the most cited and productive authors, countries and subject areas related to Big Data. Lastly, a science map is performed to understand the intellectual structure and the main research lines (themes)

Stable capillary hypersurfaces and the partitioning problem in balls with radial weights

In a round ball B ⊂ Rn+1 endowed with an O(n+1)-invariant metric we consider a radial function that weights volume and area. We prove that a compact two-sided hypersurface in B which is stable capillary in weighted sense and symmetric about some line containing the center of B is homeomorphic to a closed n-dimensional disk. When combined with Hsiang symmetrization and other stability results this allows to deduce that the interior boundary of any isoperimetric region in B for the Gaussian weight is a closed n-disk of revolution. For n = 2 we also show that a compact weighted stable capillary surface in B of genus 0 is a closed disk of revolution

Stable and isoperimetric regions in some weighted manifolds with boundary

In a Riemannian manifold with a smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of the weighted perimeter under variations preserving the weighted volume. By assuming local convexity of the boundary and certain behavior of the Bakry–Émery– Ricci tensor we deduce rigidity properties for stable sets by using deformations constructed from parallel vector fields tangent to the boundary. As a consequence, we completely classify the stable sets in some Riemannian cylinders Ω × R with product weights. Finally, we also establish uniqueness results showing that any minimizer of the weighted perimeter for fixed weighted volume is bounded by a horizontal slice Ω × {t}.MINECO, Spain MTM2017-84851-C2-1-PJunta de Andalucía European Commission FQM32

Compact anisotropic stable hypersurfaces with free boundary in convex solid cones

We consider a convex solid cone C in R^{n+1} with vertex at the origin and boundary smooth away from 0. Our main result shows that a compact two-sided hypersurface Sigma immersed in C with free boundary away from 0 and minimizing, up to second order, an anisotropic area functional under a volume constraint is contained in a Wulff-shape. The technique of proof also works for a non-smooth convex cone C provided the boundary of Sigma is away from the singular set of the boundary of C.Grant PID2020-118180GB-I00 funded by MCIN/AEI/10.13039/501100011033Junta de Andalucía grant PY20-0016