A gap theorem on complete shrinking gradient Ricci solitons

Abstract

In this short note, using Günther's volume comparison theorem and Yokota's gap theorem on complete shrinking gradient Ricci solitons, we prove that for any complete shrinking gradient Ricci soliton (M n

On the structure of Ricci shrinkers

“…Zhang(c.f. [55]). However, Theorem 1.3 is based on a very different proof, which will be provided as follows to conclude this section.…”

Small curvature concentration and Ricci flow smoothing

“…Theorem 1.3. For all A > 0, there is ε(n, A) > 0 such that if (M n , g, f ) is a complete shrinking or steady gradient Ricci soliton satisfying Gap results for gradient Ricci solitons have been previously studied for instance in [59,20,61] under global assumptions on the potential function f , sometimes along with pointwise curvature control (see also [41,15,19,7] ).…”