27 research outputs found
A note on the index of closed minimal hypersurfaces of flat tori
Generalizing earlier work by Ros in ambient dimension three, we prove an affine lower bound for the Morse index of closed minimal hypersurfaces inside a flat torus in terms of their first Betti number (with purely dimensional coefficients)
Compactness analysis for free boundary minimal hypersurfaces
We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control
Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and p-th Jacobi Eigenvalue
Given a closed Riemannian manifold of dimension less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on the p-th Jacobi eigenvalue for p≥2 one gains strong convergence to a smooth limit submanifold away from at most p−1 points
Bubbling analysis and geometric convergence results for free boundary minimal surfaces
We investigate the limit behaviour of sequences of free boundary minimal hypersurfaces with bounded index and volume, by presenting a detailed blow-up analysis near the points where curvature concentration occurs. Thereby, we derive a general quantization identity for the total curvature functional, valid in ambient dimension less than eight and applicable to possibly improper limit hypersurfaces. In dimension three, this identity can be combined with the Gauss-Bonnet theorem to provide a constraint relating the topology of the free boundary minimal surfaces in a converging sequence, of their limit, and of the bubbles or half-bubbles that occur as blow-up models. We present various geometric applications of these tools, including a description of the behaviour of index one free boundary minimal surfaces inside a 3-manifold of non-negative scalar curvature and strictly mean convex boundary. In particular, in the case of compact, simply connected, strictly mean convex domains in R3 unconditional convergence occurs for all topological types except the disk and the annulus, and in those cases the possible degenerations are classified
Effect of Systemic Hypertension With Versus Without Left Ventricular Hypertrophy on the Progression of Atrial Fibrillation (from the Euro Heart Survey).
Hypertension is a risk factor for both progression of atrial fibrillation (AF) and development of AF-related complications, that is major adverse cardiac and cerebrovascular events (MACCE). It is unknown whether left ventricular hypertrophy (LVH) as a consequence of hypertension is also a risk factor for both these end points. We aimed to assess this in low-risk AF patients, also assessing gender-related differences. We included 799 patients from the Euro Heart Survey with nonvalvular AF and a baseline echocardiogram. Patients with and without hypertension were included. End points after 1 year were occurrence of AF progression, that is paroxysmal AF becoming persistent and/or permanent AF, and MACCE. Echocardiographic LVH was present in 33% of 379 hypertensive patients. AF progression after 1 year occurred in 10.2% of 373 patients with rhythm follow-up. In hypertensive patients with LVH, AF progression occurred more frequently as compared with hypertensive patients without LVH (23.3% vs 8.8%, p = 0.011). In hypertensive AF patients, LVH was the most important multivariably adjusted determinant of AF progression on multivariable logistic regression (odds ratio 4.84, 95% confidence interval 1.70 to 13.78, p = 0.003). This effect was only seen in male patients (27.5% vs 5.8%, p = 0.002), while in female hypertensive patients, no differences were found in AF progression rates regarding the presence or absence of LVH (15.2% vs 15.0%, p = 0.999). No differences were seen in MACCE for hypertensive patients with and without LVH. In conclusion, in men with hypertension, LVH is associated with AF progression. This association seems to be absent in hypertensive women
Progression From Paroxysmal to Persistent Atrial Fibrillation. Clinical Correlates and Prognosis
Objectives: We investigated clinical correlates of atrial fibrillation (AF) progression and evaluated the prognosis of patients demonstrating AF progression in a large population. Background: Progression of paroxysmal AF to more sustained forms is frequently seen. However, not all patients will progress to persistent AF. Methods: We included 1,219 patients with paroxysmal AF who participated in the Euro Heart Survey on AF and had a known rhythm status at follow-up. Patients who experienced AF progression after 1 year of follow-up were identified. Results: Progression of AF occurred in 178 (15%) patients. Multivariate analysis showed that heart failure, age, previous transient ischemic attack or stroke, chronic obstructive pulmonary disease, and hypertension were the only independent predictors of AF progression. Using the regression coefficient as a benchmark, we calculated the HATCH score. Nearly 50% of the patients with a HATCH score >5 progressed to persistent AF compared with only 6% of the patients with a HATCH score of 0. During follow-up, patients with AF progression were more often admitted to the hospital and had more major adverse cardiovascular events. Conclusions: A substantial number of patients progress to sustained AF within 1 year. The clinical outcome of these patients regarding hospital admissions and major adverse cardiovascular events was worse compared with patients demonstrating no AF progression. Factors known to cause atrial structural remodeling (age and underlying heart disease) were independent predictors of AF progression. The HATCH score may help to identify patients who are likely to progress to sustained forms of AF in the near future. \ua9 2010 American College of Cardiology Foundation
Geometric convergence results for closed minimal surfaces via bubbling analysis
We present some geometric applications, of global character, of the bubbling analysis developed by Buzano and Sharp for closed minimal surfaces, obtaining smooth multiplicity one convergence results under upper bounds on the Morse index and suitable lower bounds on either the genus or the area. For instance, we show that given any Riemannian metric of positive scalar curvature on the three-dimensional sphere the class of embedded minimal surfaces of index one and genus γ is sequentially compact for any γ≥1. Furthemore, we give a quantitative description of how the genus drops as a sequence of minimal surfaces converges smoothly, with mutiplicity m≥1, away from finitely many points where curvature concentration may happen. This result exploits a sharp estimate on the multiplicity of convergence in terms of the number of ends of the bubbles that appear in the process
Combined experimental and computational 1H NMR study of water adsorption onto graphenic materials
The effects caused by the interaction with graphene-like layers on the 1H NMR spectra of water molecules adsorbed onto porous carbon materials were investigated by a combination of shielding calculations using density functional theory (DFT) and 1H NMR experiments. Experimental 1H NMR spectra were recorded for different water-containing carbon materials (activated carbons and milled graphite samples); the 1H NMR signals due to adsorbed water in these materials showed a strong shielding effect caused by the electron currents present in the graphene-like layers. This effect was enhanced for activated carbons prepared at high heat treatment temperatures and for milled graphite samples with short milling times, evidencing that the structural organization of the graphene-like layers was the key feature defining the magnitude of the shielding on the 1H nuclei in the water molecules adsorbed by the analyzed materials. The DFT calculations of the shielding sensed by these 1H nuclei showed an increased interaction with the graphitic layers as the distance between these layers (representing the pore size) was reduced. A continuous decrease of the 1H NMR chemical shift was then predicted for pores of smaller sizes, in good agreement with the experimental findings. These calculations also showed a large dispersion of chemical shifts for the several 1H nuclei in the water clusters, attributed to intermolecular interactions and to shielding variations within the pores. This dispersion, combined with the effects due to the locally anisotropic diamagnetic susceptibility of graphite-like crystallites, are the main contributions to the broadening of the 1H NMR signals associated with water adsorbed onto porous carbon materials
Black hole topology in f(R) gravity
Hawking's topology theorem in general relativity restricts the cross-section of the event horizon of a black hole in 3+1 dimension to be either spherical or toroidal. The toroidal case is ruled out by the topology censorship theorems. In this article, we discuss the generalization of this result to black holes in f(R) gravity in 3+1 and higher dimensions. We obtain a sufficient differential condition on the function f'(R), which restricts the topology of the horizon cross-section of a black hole in f(R) gravity in 3+1 dimension to be either S^2 or S^1× S^1. We also extend the result to higher dimensional black holes and show that the same sufficient condition also restricts the sign of the Yamabe invariant of the horizon cross-section.by Akash K Mishra, Mostafizur Rahman and Sudipta Sarka