讲座题目：A class problem of k-curvature

讲座摘要：In this talk, We first introduce the rigidity problem on closed locally conformally flat manifolds with constant $k$-curvature or constant quotient curvature. We prove that such manifolds must have constant sectional curvature under the assumption that the manifolds have nonnegative sectional curvature and the modified Schouten tensor is k-admissible, Moreover, when k=2, the assumption can be instead of nonnegative Ricci curvature. The same result is also held on closed locally conformally flat manifolds with totally geodesic boundary. Then, we consider the soliton problems related to fully nonlinear type Yamabe flow on both closed manifold and compact manifold with boundary. we prove that any k-Yamabe soliton or quotient Yamabe soliton must have constant  k-curvature or quotient curvature on closed locally conformally flat manifolds and compact closed locally conformally flat manifolds with totally geodesic boundary.

讲座时间：2019年6月5日下午2:00-3:00

讲座地点：勤园21楼306

主讲人：薄乐阳博士

主讲人简介：薄乐阳，浙江大学博士，研究方向为几何分析，博士期间的研究兴趣集中共形几何特别是紧致流形上与k曲率相关的刚性问题。在此方面，薄乐阳博士与合作者得到如下结果：1，对于局部共形平坦的具有常k曲率的流形，如果其截面曲率为正，则流形一定具有常截面曲率；2，局部共形平坦流形中具有正的k-曲率的Yamabe soliton必然具有常k曲率。