The Li-Yau-Hamilton Estimate and the Yang-Mills Heat Equation on Manifolds with Boundary
The paper pursues two connected goals. Firstly, we establish the Li-Yau-Hamilton estimate for the heat equation on a manifold $M$ with nonempty boundary. Results of this kind are typically used to prove monotonicity formulas related to geometric flows. Secondly, we establish bounds for a solution $\nabla(t)$ of the Yang-Mills heat equation in a vector bundle over $M$. The Li-Yau-Hamilton estimate is utilized in the proofs. Our results imply that the curvature of $\nabla(t)$ does not blow up if the dimension of $M$ is less than 4 or if the initial energy of $\nabla(t)$ is sufficiently small.
Global existence and convergence of smooth solutions to Yang-Mills gradient flow over compact four-manifolds
In this monograph we develop results on global existence and convergence of solutions to the gradient flow equation for the Yang-Mills energy functional on a principal bundle, with compact Lie structure group, over a closed, four-dimensional, Riemannian, smooth manifold, including the following. If the initial connection is close enough to a minimum of the Yang-Mills energy functional, in a norm or energy sense, then the Yang-Mills gradient flow exists for all time and converges to a Yang-Mills connection. If the initial connection is allowed to have arbitrary energy but we restrict to the setting of a Hermitian vector bundle over a compact, complex, Hermitian (but not necessarily Kaehler) surface and the initial connection has curvature of type $(1,1)$, then the Yang-Mills gradient flow exists for all time, though bubble singularities may (and in certain cases must) occur in the limit as time tends to infinity. The Lojasiewicz-Simon gradient inequality plays a crucial role in our approach and we develop two versions of that inequality for the Yang-Mills energy functional.
Pharmacokinetics of Mivacurium Isomers and Their Metabolites in Healthy Volunteers after Intravenous Bolus Administration
Background Previous studies report the pharmacokinetics of mivacurium isomers after an infusion using venous blood sampling. Although the extent of the mivacurium arterial‐venous gradient is not known, the sampling site is likely to influence mivacurium pharmacokinetic parameters because the drug is rapidly metabolized as it traverses the circulation. The objectives of this study were (1) to determine the pharmacokinetics of mivacurium isomers in healthy persons after intravenous bolus administration using intensive arterial blood sampling, and (2) to characterize the formation and elimination of mivacurium metabolites in human plasma. Methods Eight persons classified as American Society of Anesthesiologists physical status 1 or 2 who were scheduled to undergo elective surgery under balanced anesthesia received 0.15 mg/kg mivacurium chloride as an intravenous bolus. Arterial blood samples were collected every 10 s during the first 2 min and at frequent intervals for 4 h thereafter. Plasma concentrations of mivacurium isomers and their metabolites were determined by two stereoselective high‐performance liquid chromatographic methods coupled with fluorometric detection and noncompartmental pharmacokinetic parameters. Results Mean elimination half‐lives of the trans‐trans, cis‐trans, and cis‐cis isomers were 2.4, 2, and 28.5 min, respectively, with corresponding mean plasma clearances of 29.2, 45.7, and 6.7 ml [center dot] min‐1 [center dot] kg‐1. The volumes of distribution at steady state of the trans‐trans, cis‐trans, and cis‐cis isomers were 0.047, 0.054, and 0.189 l/kg, respectively. Plasma concentrations of monoester and alcohol metabolites peaked 25 s (median) after mivacurium injection, with half‐lives in the range of 90 min, except for the cis alcohol metabolite, which was only negligibly and transiently formed. Conclusions Substantial hydrolysis of mivacurium isomers by cholinesterases was confirmed by the rapid appearance of mivacurium metabolites in plasma. The intensive arterial sampling proved to be critical for the trans‐trans and cis‐trans isomers because the area under the curve between 0 and 2 min accounted for 75% and 86% of the total, respectively.