In this paper, we describe the structure of isotropy subgroups some almost rigid domains and give necessary sufficient conditions for an automorphism to be element subgroup.

We constrain the distribution of merging compact binaries across celestial sphere using GWTC-3 catalog from LIGO-Virgo-KAGRA Collaborations' (LVK) third observing run. With 63 confident detections O3, we relative variability (standard deviation) rate density sky to be $\lesssim 16\%$ at 90\% confidence assuming logarithm is described by a Gaussian random field with correlation length $\geq 10^\...