Title：The quaternionic Monge-Amp\`{e}re operator and closed positive currents  over the Heisenberg group

Speaker：王 伟   （浙江大学） 

Time：2021年5月30日，周日，上午   9:00-10:00 

Room：科大东区 第五教学楼5207

Abstract：Some fundamental results of the quaternionic pluripotential theory on $\mathbb{H}^n$ are extended to the Heisenberg group. We introduce  notions of a plurisubharmonic function, the quaternionic Monge-Amp\`{e}re operator,  differential operators $d_0$ and $d_1$ acting on the quaternionic version of differential forms, and a closed positive current on the Heisenberg group. The quaternionic Monge-Amp\`{e}re operator is the coefficient of the exterior product of $\triangle u=d_0d_1u$. The Chern-Levine-Nirenberg type estimate is established and the definition of quaternionic Monge-Amp\`{e}re operator is extended to continuous quaternionic plurisubharmonic functions. The minimun principle for this operator is also established.

王伟，浙江大学数学学院教授，博士生导师。研究方向为多复变函数论。近年来的研究集中在将多变量复分析拓展到一些具有特殊代数结构或几何结构的空间上，例如多个四元变量的函数论。