Rigidity of volume-minimizing hypersurfaces in Riemannian 5-manifolds

In this paper we generalize the main result of [4] for manifolds that are not necessarily Einstein. In fact, we obtain an upper bound for the volume of a locally volume-minimizing closed hypersurface $\Sigma$ of a Riemannian 5-manifold $M$ with scalar curvature bounded from below by a positive constant in terms of the total traceless Ricci curvature of $\Sigma$. Furthermore, if $\Sigma$ saturates the respective upper bound and $M$ has nonnegative Ricci curvature, then $\Sigma$ is isometric to $\mathbb{S}^4$ up to scaling and $M$ splits in a neighborhood of $\Sigma$. Also, we obtain a rigidity result for the Riemannian cover of $M$ when $\Sigma$ minimizes the volume in its homotopy class and saturates the upper bound.Comment: 9 pages. Minor changes. Version to appear in Math. Proc. Cambridge Philos. Societ

On History and Liberty: The ‘Revisionism’ of Bronisław Baczko

The ‘Warsaw School of History of Ideas’ is the name given to a ‘revisionist think tank’ which was led by the historian Bronisław Baczko from 1956 to 1968 in Communist Poland. This group reunited scholars like Leszek Kołakowski or Krzysztof Pomian around questions related to political believes, theological conceptions or utopian thought. Expelled from the University, B. Baczko left Poland and seek shelter in Geneva where he became a Professor of history of Ideas and historiography. In his new home, he developed an original vision on Enlightenment and the French Revolution