26 citations · 27 across the 7 of their papers we have counts for
6 papers · 1 filter
On a conformal gap and finiteness theorem for a class of four manifolds
Alice Chang, Jie Qing, Paul Yang
In 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. Applyin…
An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature
Sun-Yung A. Chang, Matthew J. Gursky, Paul C. Yang
We formulate natural conformally invariant conditions on a 4-manifold for the existence of a metric whose Schouten tensor satisfies a quadratic inequality. This inequality implies…
A conformally invariant sphere theorem in four dimensions
S. Y. A Chang, Matthew J. Gursky, Paul Yang
In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 ineq…
On the topology of conformally compact Einstein 4-manifolds
Alice Chang, Jie Qing, Paul Yang
In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also posit…
On finiteness of Kleinian groups in general dimension
Alice Chang, Jie Qing, Paul Yang
In this paper we provide a criteria for geometric finiteness of Kleinian groups in general dimension. We formulate the concept of conformal finiteness for Kleinian groups in space…
Non-linear partial differential equations in conformal geometry
Sun-Yung Alice Chang, Paul C. Yang
In the study of conformal geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a f…