Seminar| Institute of Mathematical Sciences
Time：Friday, November 12th, 2021, 14:00-15:00
Location：R408, IMS
Speaker: Jingchen Hu, China Academy of Science
Abstract: The homogeneous complex Monge-Ampere equation (HCMA) arises very naturally in several complex variables and Kahler geometry, and the existence and the regularity of the solutions have been extensively studied by many authors. It is known that solutions to the HCMA equation fail to be C2 in general, since the equation is degenerate and the best regularity is C1,1 by examples of Bedford-Forneass and Lempert-LizVivas. However as observed by Donaldson, in many situations the solutions have better regularity and possess foliation structure. One of the most important step in establishing the foliation structure is the estimate of the second smallest eigenvalue of the Hessian of a solution. In this talk, we discuss a new method of estimating the second smallest eigenvalue and its application in some geometry and several complex variables problems.