Positive Ricci curvature through Cheeger deformation

Let $(M,g)$ be a Riemannian manifold with an isometric $G$-action. If a principal orbit has finite fundamental group and $\mathrm{Ric}_{M^{reg}/G}\geq 1$, Searle--Wilhelm proved that $M$ admits a new metric $\tilde g$ of positive Ricci curvature. $\tilde g$ is obtained after a conformal change followed by a Cheeger deformation. The question remained on whether it is sufficient to consider only the Cheeger deformation to attain positive Ricci curvature on the new metric $\tilde g$. Here we approach this question by giving necessary and sufficient conditions on the $G$-action. In particular, we construct an infinite family of manifolds satisfying the hypothesis of Searle--Wilhelm that do not develop positive Ricci curvature after Cheeger deformation. Further exploring the theory, we give a alternative proofs for Lawson--Yau result on positive scalar curvature under non-abelian symmetry, among others.Comment: 26 pages. Exposition reviewed. Applications include

An innovative platform for territorial marketing and location benchmarking

When looking for locations to install their production or business units, entrepreneurs undertake a well established decision process that starts with the very first option to invest in a specific country and finishes with a final decision over a commonly named “short list”. In order to support investors looking for investment locations in Portugal across the decision process mentioned before, an internet platform was developed and deployed worldwide as a result of a development partnership between the University of Minho and Innovation Point S.A., a technological start-up. The platform, named where-to-invest-in-portugal.com and often classified as a territorial marketing & analysis platform, includes an extensive set of resources to support potential investors. Among them, the so-called Investor_DSS channel is a multicriteria Decision Support System intended to model the geographical screening and find the best ranked set of locations (municipalities) for a particular location exercise. Other channels include fact sheets and databases for Business Space Offers and Business Opportunities. A special channel is dedicated to the Mayors, a space where they may address an invitation for direct investment in their Municipalities. This paper describes the architecture of the platform and some of the relevant developments related to

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.244112

Estado de mal epiléptico por crise parcial complexa em uma criança

Complex partial status epilepticus (SE) has been reported rarely in children. We describe the clinical case of a 14 year-old girl with complex partial seizures (CPS) since age 10 who developed a complex partial SE probably because she was not adherent to treatment. The neurologic examination and computed tomography scan were normal. During the SE she received diazepam and phenytoin and became free of the seizures after 5 minutes. The ictal EEG showed spikes and slow waves over the right temporal region.Estado de mal epiléptico por crise parcial complexa tem sido raramente referido em crianças. Relatamos o quadro clínico de uma menina com 14 anos de idade, com crises parciais complexas desde os 10 anos e que desenvolveu estado de mal epiléptico por crises parciais complexas, provavelmente por não ser aderente ao tratamento. O exame neurológico e a tomografia computadorizada de crânio foram normais. Durante o estado de mal epiléptico ela recebeu fenitoína e diazepam e ficou livre das crises após 5 minutos. O EEG ictal mostrou espículas e ondas lentas na região temporal direita.Escola Paulista de Medicina EEG SectorEPMUNIFESP, EPM, EEG SectorEPMSciEL

Reversão de dipolo: um achado crítico em um paciente com epilepsia parcial benigna da infância com ponta centrotemporal

We describe the case of a 15-year-old boy who had the diagnosis of benign partial epilepsy of childhood with centrotemporal spike. During the EEG a subclinical electrographic seizure was recorded. The discharges were clearly electropositive in T4 with positive phase reversal between derivations F8-T4 and T4-T6. The whole episode lasted less than one minute (45 sec). The interictal right medio-temporal spikes reemerged after 60 sec and were electronegative in the same location after the end of the electrographic seizures. The mechanisms underlying this uncommon pattern on EEG is not well stablished.Relatamos o caso de um menino de 15 anos com o diagnóstico de epilepsia parcial benigna da infância com ponta centrotemporal. Durante o EEG uma crise eletrográfica subclínica foi gravada. As descargas estavam eletropositivas em T4 com reversão de fase positiva entre as derivações F8-T4 e T4-T6. O episódio durou menos que um minuto (45 seg). As espículas inter-ictais, na região temporal média direita, reapareceram 60 seg após e estavam eletronegativas na mesma região depois do término da crise eletrográfica. O mecanismo subjacente a este padrão incomum no EEG não está bem estabelecido.Escola Paulista de Medicina EEG SectorEPMUNIFESP, EPM, EEG SectorEPMSciEL

Descarga eletrográfica rítmica subclínica do adulto: uma evolução atípica

The subclinical rhythmic electrographic discharge in adults (SREDA) has been rarely reported. We describe the case of a 71 year-old man with transient ischemic attack, whose EEG showed an atypical evolution of this uncommon pattern. The computed tomography scan and cerebrospinal fluid were normal. We are not aware of any other report in the literature with this atypical evolution of SREDA.A descarga eletrográfica rítmica subclínica do adulto tem sido raramente referida na literatura. Relatamos o caso de um homem de 71 anos com ataque isquêmico transitório, cujo EEG mostrou evolução atípica deste padrão incomum. A tomografia computadorizada de crânio e o liquido cefalorraquidiano foram normais. Na literatura por nós pesquisada, não achamos outra publicação com evolução atípica do SREDA.Escola Paulista de Medicina EEG SectorUNIFESP, EPM, EEG SectorSciEL