A renormalized index theorem for some complete asymptotically regular metrics: The Gauss–Bonnet theorem

A Renormalized Index Theorem for Some Complete Asymptotically Regular Metrics: the Gauss-bonnet Theorem

The Gauss-Bonnet Theorem is studied for edge metrics as a renormalized index theorem. These metrics include the Poincaré-Einstein metrics of the AdS/CFT correspondence. Renormalization is used to make sense of the curvature integral and the dimensions of the L-cohomology spaces as well as to carry out the heat equation proof of the index theorem. For conformally compact metrics even mod x, the ...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

The Morse index theorem for regular Lagrangian systems

In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.

Some Results on Baer's Theorem

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

The index theorem of regular variation and its applications

We develop further the topological theory of regular variation of [BOst13]. There we established the uniform convergence theorem (UCT) in the setting of topological dynamics (i.e. with a group T acting on a homogenous space X), thereby unifying and extending the multivariate regular variation literature. Here, working with realtime topological ‡ows on homogeneous spaces, we identify an index of...