A quantitative version of strong localization the Kobayashi, Azukawa and Sibony metrics, as well squeezing function, near a plurisubharmonic peak boundary point domain in $${\mathbb {C}}^n$$ is given. As an application, behavior these metrics strictly pseudoconvex studied. weak three function also given antipeak point.

We study invariant and bi-invariant metrics on groups focusing finite G . show that non-equivalent (bi) are in 1-1 correspondence with unitary symmetric (conjugate) partitions To every metric group ( , d ) we associate to it the symmetry weighted graph of distances. Using these objects can classify all equivalence classes for small groups. then number give an expression such terms Bell numbers,...

This article investigates stochastic invariance for control systems through probabilistic controlled invariant sets (PCISs). As a natural complement to robust (RCISs), we propose finite-, and infinite-horizon PCISs, explore their relation RICSs. We design iterative algorithms compute the PCIS within given set. For with discrete spaces, computations of PCISs at each iteration are based on linear...

We provide techniques for studying the nonnegatively curved leftinvariant metrics on a compact Lie group. For “straight” paths of left-invariant metrics starting at bi-invariant metrics and ending at nonnegatively curved metrics, we deduce a nonnegativity property of the initial derivative of curvature. We apply this result to obtain a partial classification of the nonnegatively curved left-inv...

Let Dn be the generalized unit disk of degree n. In this paper, we compute Riemannian metrics on Dn × C (m,n) which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.