Entropies, volumes, and Einstein metrics

We survey the definitions and some important properties of several asymptotic invariants of smooth manifolds, and discuss some open questions related to them. We prove that the (non-)vanishing of the minimal volume is a differentiable property, which is not invariant under homeomorphisms. We also formulate an obstruction to the existence of Einstein metrics on four-manifolds involving the volume entropy. This generalizes both the Gromov--Hitchin--Thorpe inequality and Sambusetti's obstruction.Comment: This is a substantial revision and expansion of the 2004 preprint, which I prepared in spring of 2010 and which has since been published. The version here is essentially the published one, minus the problems introduced by Springer productio

A simple proof of Perelman's collapsing theorem for 3-manifolds

We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained, accessible to non-experts and advanced graduate students. Perelman's collapsing theorem for 3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our arguments in the earlier arXiv version. v2: added one more grap

Thermophysical behavior of three algal biodiesels over wide ranges of pressure and temperature

ACLInternational audienc

Heat capacity of 1-pentylamine and 1-hexylamine: Experimental determination and modeling through a two-state association model (TSAM)

International audienceWe report new experimental data of heat capacity of two primary amines, namely 1-pentylamine and 1-hexylamine over wide ranges of pressure [0.1-60 (MPa)] and temperature [303.15-403.15 (K)]. The experimental behaviour of the heat capacity versus temperature and pressure is analyzed. An attempt to rationalize this behaviour is performed through a two-state association model (TSAM), which allows expressing the specific effect due to association at molecular level. It appears that the heat capacity trend versus temperature is clearly governed by auto-association between amines molecules. The physical meaningful of the (TSAM) model parameters highlights the capability of this approach to capture the heat capacity behavior of the amines

Positive streamer formation in cathode region of pulsed high-pressure discharges for transversely excited atmosphere laser applications

International audienc

Les instantanés, croquis et impressions de voyage d'un métromane. T. 1 / L.-D. Bessières

Contient une table des matière