Isoperimetric inequalities in Euclidean convex bodies

In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a convex body, i.e., a compact convex set in Euclidean space with interior points. We shall not impose any regularity assumption on the boundary of the convex set. Amongst other results, we shall prove the equivalence between Hausdorff and Lipschitz convergence, the continuity of the isoperimetric profile with respect to the Hausdorff distance,and the convergence in Hausdorff distance of sequences of isoperimetric regions and their free boundaries. We shall also describe the behavior of the isoperimetric profile for small volume, and the behavior of isoperimetric regions for small volume.Comment: Final version. References and a dedication adde

Large isoperimetric regions in the product of a compact manifold with Euclidean space

Given a compact Riemannian manifold $M$ without boundary, we show that large isoperimetric regions in $M\times\mathbb{R}^k$ are tubular neighborhoods of $M\times\{x\}$, with $x\in\mathbb{R}^k$.Comment: Final version, to appear in Adv. Mat

Foreword

Presentation of JSSE 57 general issue.

Performative betrayals: Christian gender politics or Christianity on trial in Oscar Wilde's Salomé

Oscar Wilde’s symbolist drama Salomé (1892) was written directly in French, a language the playwright “adore[d] without speaking it well” (Ellmann).  In order to avoid awkward phrasing in the dialogues, Wilde minimized the importance of language in favour of the show. In consequence in Salomé silence is at least as important as speech, and showing or suggesting through performance makes up for telling. The eponymous heroine is therefore mainly shaped by quotations. These are either stated by third characters or “translated” into images through performance. The enunciated quotations epitomize the male characters’ gaze while the “performed” ones, which are actually scraps and bits from Biblical, Greek and Roman myths, are more inherent with Salome’s “essential nature”. Consequently, in this gender-oriented drama, Salomé appears as a discursive and plastic construct which brings together male representations of the feminine as both an ideal and a threat  (notably the 19th century myth of the femme fatale) as well as performative evocations of archetypal female characters (such as Isis, Ishtar). The above characterization process aims at opposing two versions of a Janus-faced Salomé, whose identity can either be  a man’s issue lying outside her control , or  an embodiment of the archetypal  matriarchal female. In both cases, Salomé functions as a self conscious postmodern construct whose self is shaped by texts and narratives.  However, when Herod is imploring her not to listen to her mother and to ask for something else than Jokanaan’s head, she answers:  “It is not my mother’s voice that I heed. It is for mine own pleasure that I ask the head of Jokanaan”.  By so doing, Salomé breaks with the tradition she stems from, both biblical and mythological, and attempts to start a new one in which pleasure becomes a yardstick by which she defines herself for us who are invited to use it, too, in order to redefine  identity and gender.