Search results for "space"

Testing the Sobolev property with a single test plan

2020

We prove that in a vast class of metric measure spaces (namely, those whose associated Sobolev space is separable) the following property holds: a single test plan can be used to recover the minimal weak upper gradient of any Sobolev function. This means that, in order to identify which are the exceptional curves in the weak upper gradient inequality, it suffices to consider the negligible sets of a suitable Borel measure on curves, rather than the ones of the $p$-modulus. Moreover, on $\sf RCD$ spaces we can improve our result, showing that the test plan can be also chosen to be concentrated on an equi-Lipschitz family of curves.

Monotonicity Formulas for Harmonic Functions in RCD(0,N) Spaces

2023

We generalize to the RCD(0,N) setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with nonnegative Ricci curvature. Rigidity and almost rigidity statements are also proven, the second appearing to be new even in the smooth setting. Motivated by the recent work in Agostiniani et al. (Invent. Math. 222(3):1033–1101, 2020), we also introduce the notion of electrostatic potential in RCD spaces, which also satisfies our monotonicity formulas. Our arguments are mainly based on new estimates for harmonic functions in RCD(K,N) spaces and on a new functional version of the ‘(almost) outer volume cone implies (almost) outer metric…

Semigenerated Carnot algebras and applications to sub-Riemannian perimeter

2021

This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic: such a phenomenon happens if and only if the semigroup generated by each horizontal half-space is a vertical half-space. We call semigenerated those Carnot groups with this property. For Carnot groups of nilpotency step 3 we provide a complete characterization of semigeneration in terms of whether such groups do not have any Engel-type quotients. Engel-type groups, which are introduced here, are the minimal (in terms of quotients) counterexamples. In add…

La diffusion des sites internet en .fr dans l'espace périurbain et rural français

2000

ACL; International audience; II existe à l'heure actuelle très peu d'études sur la localisation et la diffusion des sites Internet compte tenu de la rareté des sources qui n'intègrent pas pour la plupart la dimension géographique (échelle nationale). A partir des fichiers de l'AFNIC, il est possible de spatialiser l'implantation des sites Internet uniquement à l'échelle des codes postaux. Pour évaluer la situation de la diffusion des sites Internet en milieu rural, le zonage en aire urbaine (ZAU) fournit une grille spatiale d'analyse pertinente.En août 1999, seulement 10 % des 40 000 sites recensés sont localisés en zone rurale et autant en milieu périurbain. Le réseau des petites villes (d…

Generalized dimension estimates for images of porous sets in metric spaces

2016

Generalized dimension distortion under Sobolev mappings

2011

CCDC 2153375: Experimental Crystal Structure Determination

2022

Related Article: María Vicent-Morales, María Esteve-Rochina, Joaquín Calbo, Enrique Ortí, Iñigo J. Vitórica-Yrezábal, Guillermo Mínguez Espallargas|2022|J.Am.Chem.Soc.|144|9074|doi:10.1021/jacs.2c01957

CCDC 782553: Experimental Crystal Structure Determination

2016

Related Article: Hélène Bertrand, Anton Granzhan, David Monchaud, Nicolas Saettel, Régis Guillot, Sarah Clifford, Aurore Guédin, Jean-Louis Mergny, Marie-Paule Teulade-Fichou|2011|Chem.-Eur.J.|17|4529|doi:10.1002/chem.201002810

Interpersonal Distance in the SARS-CoV-2 Crisis

2020

Background Mandatory rules for social distancing to curb the SARS-CoV-2 pandemic require individuals to maintain a critical interpersonal distance above 1.5 m. However, this contradicts our natural preference, which is closer to 1 m for non-intimate encounters, for example, when asking a stranger for directions. Objective This review addresses how humans typically regulate interpersonal distances, in order to highlight the challenges of enforcing atypically large interpersonal distances. Method To understand the challenges posed by social distancing requirements, we integrate relevant contributions from visual perception, social perception, and human factors. Results To date, research on pr…

Too close for comfort? The impact of salesperson‐customer proximity on consumers' purchase behavior

2021

Across a series of lab and field studies, with a total sample of over 1200 participants, we investigate how the physical proximity between salespeople and customers can impact store loyalty, purchase intentions, and actual spending. An initial survey among a representative sample of retail salespeople reveals that they associate close physical proximity between employees and customers with positive consumer outcomes, an intuition that dovetails with prior research documenting the positive influence of such proximity on purchase intentions, particularly in nonexpressive consumption contexts. Contrary to this work, we demonstrate, across four studies in which proximity was both measured and m…