TY - JOUR AU - Chang, Sun-Yung Alice AU - Chen, Eric PY - 2021/09/19 Y2 - 2024/03/29 TI - Some aspects of Ricci flow on the 4-sphere JF - New Zealand Journal of Mathematics JA - NZ J Math VL - 52 IS - SE - Vaughan Jones Memorial Special Issue DO - 10.53733/152 UR - https://nzjmath.org/index.php/NZJMATH/article/view/152 SP - 381--402 AB - <p>In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize the standard 4-sphere. We obtain a conformal gap theorem, and for Yamabe metrics of positive scalar curvature with L^2 norm of the Weyl tensor of the metric suitably small, we establish the monotonic decay of the L^p norm for certain p&gt;2 of the reduced curvature tensor along the normalized Ricci flow, with the metric converging exponentially to the standard 4-sphere.</p> ER -