78 research outputs found
Nonexistence of marginally trapped surfaces and geons in 2+1 gravity
We use existence results for Jang's equation and marginally outer trapped
surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity.
In particular, our results show that any 2+1 initial data set, which obeys the
dominant energy condition with cosmological constant \Lambda \geq 0 and which
satisfies a mild asymptotic condition, must have trivial topology. Moreover,
any data set obeying these conditions cannot contain a MOTS. The asymptotic
condition involves a cutoff at a finite boundary at which a null mean convexity
condition is assumed to hold; this null mean convexity condition is satisfied
by all the standard asymptotic boundary conditions. The results presented here
strengthen various aspects of previous related results in the literature. These
results not only have implications for classical 2+1 gravity but also apply to
quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have
been combined to give a single proof, thereby circumventing an issue with the
second proof associated with potential blow-ups of solutions to Jang's
equation. To appear in Commun. Math. Phy
On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications
Let be a strictly increasing function
with . We unify the concepts of -harmonic maps, minimal
hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and
introduce -Yang-Mills fields, -degree, -lower degree, and generalized
Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on
manifolds. When and
the -Yang-Mills field becomes an ordinary Yang-Mills field,
-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus
sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a
manifold respectively. We also introduce the energy functional (resp.
-Yang-Mills functional) and derive the first variational formula of the
energy functional (resp. -Yang-Mills functional) with
applications. In a more general frame, we use a unified method to study the
stress-energy tensors that arise from calculating the rate of change of various
functionals when the metric of the domain or base manifold is changed. These
stress-energy tensors, linked to -conservation laws yield monotonicity
formulae. A "macroscopic" version of these monotonicity inequalities enables us
to derive some Liouville type results and vanishing theorems for forms with
values in vector bundles, and to investigate constant Dirichlet boundary value
problems for 1-forms. In particular, we obtain Liouville theorems for
harmonic maps (e.g. -harmonic maps), and Yang-Mills fields (e.g.
generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain
generalized Chern type results for constant mean curvature type equations for
forms on and on manifolds with the global doubling property
by a different approach. The case and is due to Chern.Comment: 1. This is a revised version with several new sections and an
appendix that will appear in Communications in Mathematical Physics. 2. A
"microscopic" approach to some of these monotonicity formulae leads to
celebrated blow-up techniques and regularity theory in geometric measure
theory. 3. Our unique solution of the Dirichlet problems generalizes the work
of Karcher and Wood on harmonic map
Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.
BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362
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