Abstract: On a conformally compact Einstein manifold, we get a gap theorem about renormalized volume, which is a global invariant. Also, we get curvature estimate based on certain lower bound of Yamabe constant on conformally compact Einstein manifolds. Secondly, we give a proof of control of volume growth lower bound by Yamabe constant of conformal infinity. As an application, we give control of the curvature of the conformally compact Einstein manifold when the Yamabe constant of conformal infinity is large.It is a joint work with Professor Jie Qing and Professor Yuguang Shi.

Time: 10:10am-12:00pm, Tuesday, Oct. 28

Place: Room 29, Quan Zhai, BICMR

Speaker: Li Gang, Peking University