John-Nirenberg Radius and Collapse in Conformal Geometry

Yuxiang Li, Guodong Wei, Zhipeng Zhou

Given a positive function $u\in W^{1,n}$, we define its John-Nirenberg radius at point $x$ to be the supreme of the radius such that ${\int }_{B_t}|\nabla \log u{|}^n<{\epsilon }_0^n$ when $n>2$,…