ar X iv : 0 71 0 . 09 26 v 3 [ m at h . M G ] 2 8 Fe b 20 08 CHARACTERIZING GENERIC GLOBAL RIGIDITY

ar X iv : 0 71 2 . 09 14 v 2 [ m at h . FA ] 2 6 Fe b 20 08 CONTRACTION SEMIGROUPS ON METRIC GRAPHS

The main objective of the present work is to study contraction semigroups generated by Laplace operators on metric graphs, which are not necessarily self-adjoint. We prove criteria for such semigroups to be continuity and positivity preserving. Also we provide a characterization of generators of Feller semi-groups on metric graphs.

ar X iv : 0 71 0 . 09 26 v 1 [ m at h . M G ] 4 O ct 2 00 7 CHARACTERIZING GENERIC GLOBAL RIGIDITY

A d-dimensional framework is a graph and a map from its vertices to E d. Such a framework is globally rigid if it is the only framework in E d with the same graph and edge lengths, up to rigid motions. For which underlying graphs is a generic framework globally rigid? We answer this question by proving a conjecture by Connelly, that his sufficient condition is also necessary. The condition come...

ar X iv : 0 90 2 . 32 39 v 1 [ m at h . D G ] 1 8 Fe b 20 09 Gauge theory in higher dimensions , II

ar X iv : 0 71 0 . 20 07 v 2 [ m at h - ph ] 1 9 Fe b 20 08 The wave equation on singular space - times

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.

ar X iv : 0 90 2 . 39 12 v 1 [ m at h . G R ] 2 3 Fe b 20 09 Brent Everitt The Combinatorial Topology