Intrinsic flat convergence with bounded Ricci curvature

In this paper we address the relationship between Gromov-Hausdorff limits and intrinsic flat limits of complete Riemannian manifolds. In \cite{SormaniWenger2010, SormaniWenger2011}, Sormani-Wenger show that for a sequence of Riemannian manifolds with nonnegative Ricci curvature, a uniform upper bound on diameter, and non-collapsed volume, the intrinsic flat limit exists and agrees with the Gromov-Hausdorff limit. This can be viewed as a non-cancellation theorem showing that for such sequences, points don't cancel each other out in the limit. Here we prove a similar no-cancellation theorem, replacing the assumption of nonnegative Ricci curvature with a two-sided bound on Ricci curvature. This version corrects a mistake in the previous version of this paper (where we assume only an arbitrary lower Ricci bound) which was due to a crucial error in one of our supporting theorems for that argument.Comment: 12 pages, 1 figur

Geometric singularities and a flow tangent to the Ricci flow

We consider a geometric flow introduced by Gigli and Mantegazza which, in the case of smooth compact manifolds with smooth metrics, is tangen- tial to the Ricci flow almost-everywhere along geodesics. To study spaces with geometric singularities, we consider this flow in the context of smooth manifolds with rough metrics with sufficiently regular heat kernels. On an appropriate non- singular open region, we provide a family of metric tensors evolving in time and provide a regularity theory for this flow in terms of the regularity of the heat kernel. When the rough metric induces a metric measure space satisfying a Riemannian Curvature Dimension condition, we demonstrate that the distance induced by the flow is identical to the evolving distance metric defined by Gigli and Mantegazza on appropriate admissible points. Consequently, we demonstrate that a smooth compact manifold with a finite number of geometric conical singularities remains a smooth manifold with a smooth metric away from the cone points for all future times. Moreover, we show that the distance induced by the evolving metric tensor agrees with the flow of RCD(K, N) spaces defined by Gigli-Mantegazza.Comment: Fixed proof of Lemma 5.4, updated references to published work

A proposed method for evaluation of morphological changes in the condyle and glenoid fossa by cone beam computed tomography

The difficulty with three-dimensional analyses remains with the myriad of data that is possible to derive from a volume. The goal of this study is to report 3D changes in the temporomandibular joint in a reliable and quantifiable way. The approach included plotting specific referents on the mandibular condyle and tracking them in magnitude (mm) and direction (°) on a reference plane after superimposing the cone beams three-dimensionally on the inferior alveolar nerve canal and the lower contour of the third molar tooth germ. Two sets of measurements were compared for reliability and each measurement showed varied correlation. Linear measurements tended to be more reliable than component and angular measurements. Angular measurements were generally the least reliable. The varied reliability results are likely due to the difficulty in superimposing limited field of view (FOV) cone beam radiographs because of inadequate structures that are able to be superimposed

Poems

Poems include: The Web , by Michael Lamm and Walking, Remembering , Suellen Munn

Novel Drugs Approved in 2021-2022

This article provides an abbreviated overview of the newly Federal Drug Administration (FDA)approved novel drugs of 2021-2022 with their respective approved indication(s). The FDA serves as the governing body that regularly evaluates and approves medications that will eventually be introduced to the market for routine use. These medications include both drugs that are the same or related to previously approved products (e.g., Extended indications of priorly approved medications) and novel drugs. By definition, a novel drug is an innovative product which serves to improve quality care in patient populations with unmet or advanced medical needs to overall advance patient care and public health. This article was employed to highlight medications that may be seen in practice and to heighten overall awareness of these new drugs. From January 1, 2021, through June 13, 2022, the FDA approved 66 drugs characterized as novel (Table 1). The four drugs highlighted in this article were selected based on potential inpatient and outpatient utility, disease-state prevalence, and overall innovative medication-based treatment approaches. The four highlighted drugs are included in Table 2