A locally anisotropic geometrical model of space-time based on CMBR

We study a locally anisotropic model of General Relativity in the framework of a more general geometrical structure than the Riemannian one. In this model the observable anisotropy of the CMBR (WMAP) is represented by a tensor of anisotropy and it is included in the metric structure of space-time. As well, some interesting special cases of spaces are considered.Comment: 5 pages, 0 figures, 7th International Astronomy Conference of the Hellenic Astronomical Society, curvature and connection sections decreased, minor explanation added, fixed some typo

Sharp Nash inequalities on manifolds with boundary in the presence of symmetries

In this paper we establish the best constant $\widetilde A_{opt}(\bar{M})$ for the Trace Nash inequality on a $n-$dimensional compact Riemannian manifold in the presence of symmetries, which is an improvement over the classical case due to the symmetries which arise and reflect the geometry of manifold. This is particularly true when the data of the problem is invariant under the action of an arbitrary compact subgroup $G$ of the isometry group $Is(M,g)$, where all the orbits have infinite cardinal

Compression syndromes of the popliteal neurovascular bundle due to Baker cyst

BackgroundThe purpose of this study was to perform a comprehensive search of the literature for all studies, case reports, and series describing Baker cyst compression of the neurovascular bundle in the popliteal fossa and index their findings according to the structures compressed.MethodCase reports and series obtained after a thorough MEDLINE search were indexed according to compressed structures. Patient demographics, main findings, method of diagnosis, cyst size, outcomes, and follow-up were recorded for each publication.ResultsSigns and symptoms related to popliteal vein and tibial nerve compression were the most frequent presentation of symptomatic Baker cysts, due to the anatomic vulnerability of these structures within the popliteal fossa and their relative sensitivity to compression. Patients with tibial nerve entrapment demonstrated gastrocnemius muscle atrophy, paresthesias, and pain. Those with popliteal vein compression experienced swelling, pain, and rarely, venous thromboembolism. Isolated arterial compression, presenting with intermittent claudication, is a rare occurrence because it is a relatively stiff-walled vessel, has a higher pressure, and is located deep in the popliteal fossa. Combinations of these compression syndromes are most frequently encountered in the context of cyst rupture and resulting compartment syndrome.ConclusionsBaker cyst is an important pathology for the differential diagnosis of popliteal neurovascular compression phenomena. It has a wide spectrum of presentation, therefore requiring accurate diagnosis for proper patient management. Because Baker cyst is by definition a chronic disorder, long-term follow-up is necessary to monitor patient recovery and prevent recurrence