Willmore submanifolds of the Möbius space and a Bernstein-type theorem

We study Willmore immersed submanifoldsf: M ^m →S ⁿ into then-Möbius space, withm≥2, as critical points of a conformally invariant functionalW. We compute the Euler-Lagrange equation and relate this functional with another one applied to the conformal Gauss map of immersions intoS ⁿ . We solve a Bernestein-type problem for compact Willmore hypersurfaces ofS ⁿ , namely, if ?a ∈? ⁿ⁺² such that <γf, a > ≠ 0 onM, whereγ _f is the hyperbolic conformal Gauss map and <, > is the Lorentz inner product of? ⁿ⁺², and iff satisfies an additional condition, thenf(M) is an (n?1)-sphere.     

The conformal Gauss map of submanifolds of the Möbius space

In this paper we study the conformal geometry of immersed submanifolds of the Möbius spaceS ⁿ introducing the conformal Gauss map. In particular we relate its harmonicity to an extended notion of Willmore surface which originated from the work of Bryant. For a more detailed account the reader is referred to the Introduction.(on leave)     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Synthesis of 1,3-diaminated stereotriads via rearrangement of 1,4-diazaspiro[2.2]pentanes

The synthesis of 1,3-diaminated stereotriads via the bis-aziridination of allenes is reported. The reactive 1,4-diazaspiro[2.2]pentane intermediates undergo a mild Br?nsted acid-promoted rearrangement to yield 1,3-diaminated ketones in good yields with excellent stereocontrol. Directed reduction of the ketone can be achieved to yield a C-N/C-O/C-N stereotriad in high dr. The ability to transfer the axial chirality of the substrates to the products allows for the facile preparation of enantioenriched stereotriads from allenes in two simple steps.