Free boundary minimal hypersurfaces with spherical boundary

We first prove that a compact embedded minimal annulus in meeting two concentric spheres perpendicularly along the boundaries is part of a plane. We also prove that an embedded minimal hypersurface lying outside of a ball is part of either a catenoid or a hyperplane if it is perpendicular to the sphere along the boundary and has only one end that is asymptotic to either a catenoid if , or a hyperplane if .     

Prüfer and Morita Hulls of FCP Extensions

We examine in this paper some properties of Morita and Prüfer hulls of FCP and FIP extensions of rings. Dichotomy phenomena appear in the case of a quasi-local base ring. In the general case, we define relative supports that allow us to introduce the concept of direct factorization of an extension and to characterize these hulls.     

The minimal dimensions of faithful representations for Heisenberg Lie superalgebras

This paper aims to determine the minimal dimensions and super-dimensions of faithful representations for Heisenberg Lie superalgebras over an algebraically closed field of characteristic zero.