【摘要】
The dHYM equation is a special type of complex Hessian equations which has connection to mirror symmetry in string theory. Recently, in the smooth setting it is shown that there exists a smooth solution of the “super-critical” dHYM equation on compact K\”ahler manifolds if and only if certain Nakai-Moishezon type criterion holds. In this talk, we will focus when the NM-type criterion fails – which is the so-called “unstable” case. We will show the existence and uniqueness of solutions of the “weak” dHYM equation, where the wedge product is replaced by the non-pluripolar product. We will also discuss the convergence of the (dHYM) cotangent flow in the unstable case. Based on a joint work with Prof. Ved Datar (IISc, Bengaluru) and Prof. Jian Song (Rutgers University).
【报告人简介】
Ramesh Mete is currently an Integrated PhD student at Indian Institute of Science, Bengaluru, under the supervision of Prof. Ved V. Datar. He is interested in Complex Differential Geometry.
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