On a conformal gap and finiteness theorem for a class of four manifolds

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102206In this paper we develop a bubble tree structure for a degenerating class of Riemannian metrics satisfying some global conformal bounds on compact manifolds of dimension 4. Applying the bubble tree structure, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and a diameter bound for a family of conformal metricssatisfying a suitable curvature equation.a new Section 6. 34 pages. to appear in GAFADifferential GeometryAnalysis of PDEs53C21; 35J60On a conformal gap and finiteness theorem for a class of four manifoldstext