Abstract We study the Brownian motion on non-compact Grassmann manifold $\frac {\textbf {U}(n-k,k)} {U}(n-k)\textbf {U}(k)}$ and some of its functionals. The key point is to realize this as a matrix diffusion process, use stochastic calculus take advantage hyperbolic Stiefel fibration functional that can be understood in setting generalized area process. In particular, connection Maass Laplacia...

We prove higher order concentration bounds for functions on Stiefel and Grassmann manifolds equipped with the uniform distribution. This partially extends previous work unit sphere. Technically, our results are based logarithmic Sobolev techniques measures manifolds. Applications include Hanson–Wright type inequalities certain distance between subspaces of Rn.

This paper is a synthesis and extension of three earlier papers on $PD_4$-complexes $X$ with fundamental group $\pi$ such that $c.d.\pi=2$ has one end. Our goal to show the homotopy types complexes are determined by $\pi$, Stiefel-Whitney classes equivariant intersection pairing $\pi_2(X)$. We achieve this under further conditions $\pi$.