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- ItemOptimal elliptic Sobolev regularity near three-dimensional, multi-material Neumann vertices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Haller-Dintelmann, Robert; Höppner, Wolfgang; Kaiser, Hans-Christoph; Rehberg, Joachim; Ziegler, Günter M.We study relative stability properties of different clusters of closely packed one- and two-dimensional localized peaks of the Swift-Hohenberg equation. We demonstrate the existence of a 'spatial Maxwell' point where clusters are almost equally stable, irrespective of the number of pes involved. Above (below) the Maxwell point, clusters become more (less) stable with the increase of the number of peaks
- ItemOptimal bounds for the colored Tverberg problem(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Blagojevi´c, Pavle V.M.; Matschke, Benjamin; Ziegler, Günter M.We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of B´ar´any et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of B´ar´any & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.