On Area Comparison and Rigidity Involving the Scalar Curvature

We prove a splitting theorem for Riemannian n-manifolds with scalar curvature bounded below by a negative constant and containing certain area-minimising hypersurfaces (Theorem 3). Thus we generalise [25,Theorem 3] by Nunes. This splitting result follows from an area comparison theorem for hypersurfaces with non-positive Sigma-constant (Theorem 4) that generalises [23, Theorem 2]. Finally, we will address the optimality of these comparison and splitting results by explicitly constructing several examples

Levine's motivic comparison theorem revisited

For a field of characteristic zero, M. Levine has proved that his category of triangulated motives is equivalent to the one constructed by V. Voevodsky. In this paper we show that the strategy of Levine's proof can be applied on every perfect field to the categories of triangulated motives with rational coefficients.Comment: 40 pages, submitte

Comparison theorem of one-dimensional stochastic hybrid delay systems

The comparison theorem of stochastic differential equations has been investigated by many authors. However, little research is available on the comparison theorem of stochastic hybrid systems, which is the topic of this paper. The systems discussed is stochastic delay differential equations with Markovian switching. It is an important class of hybrid systems