The volume flux group and nonpositive curvature

We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of Kedra-Kotschick-Morita for this class of manifolds.Comment: 6 pages, final version, to appear in Ann. Global Analysis and Geometr

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

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

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Introduction à l'étude philosophique de la phrénologie et nouvelle classification des facultés cérébrales / par le Dr G.-L. Bessières

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Ocean state indicators from MyOcean altimeter products

The European MyOcean project (<a href="http://www.myocean.eu.org"http://www.myocean.eu.org"_blank">http://www.myocean.eu.org</a>) provides observations of the ocean dynamic topography from altimeter measurements. Three specific indicators have been developed, based on altimeter data only, in order to monitor the ocean state. The first ocean indicator observes the positive and negative phases of the ENSO events in the tropical Pacific, the El Niño/La Niña events, since 1992. The second ocean indicator tracks the contracted or extended state of the Kuroshio Extension. The last ocean indicator is dedicated to the Ionian Basin in the Mediterranean Sea and permits separation of "zonal-cyclonic" state (1998–2005 and since 2011 up to now) from the "anticyclonic" state (1993–1996) usually discussed in the literature. In addition, it allows identifying a third state in which both the anticyclonic circulation around the northern part of the basin and the strong zonal Mid-Ionian Jet co-exist (2008–2010)