The second Sobolev best constant along the Ricci flow

摘要

In this work we present some properties satisfied by the second Rieman-nian Sobolev best constant along the Ricci flow on compact manifolds of dimensions n > 4. We prove that, along the Ricci flow g(t), the second best constant 5o(2, g(t)) depends continuously on t and blows-up in finite time In certain cases, the speed of the explosion is, at least, the same one of the curvature operator. We also show that, on manifolds with positive curvature operator or pointwise 1 /4-pinched curvature, one of the situations holds: So(2, g(0) converges to an explicit constant or extremal functions there exists for t large.