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Nonexistence of Poincare-Einstein Fillings on Spin Manifolds
发布时间: 2017-12-19     12:01   【返回上一页】 发布人:韩青


 

北京师范大学数学科学学院

偏微分方程学术报告

 

报告题目:Nonexistence of Poincare-Einstein Fillings on Spin Manifolds

报告人:Professor Qing Han (韩青(University of Notre Dame/Peking University)

时间地点:20171225 10:00-11:00, 后主楼1223

邀请人:李海刚

报告摘要:

Graham and Fefferman raised the question whether a conformal class on the boundary M of a given compact manifold X can be the conformal infinity of a Poincare-Einstein metric in X. In this talk, we construct an invariant of conformal classes on the boundary M of a compact spin manifold X of dimension 4k with the help of the Dirac operator. We prove that a conformal class cannot be the conformal infinity of a Poincare-Einstein metric if this invariant is not zero. Furthermore, we will prove this invariant can attain values of infinitely many integers if one invariant is not zero on the above given spin manifold. This talk is based on a joint work with Gursky and Stolz.