四类典型域的Gromov辛宽度和Hofer-Zehnder辛容量

Symplectic capacities of the classical domains of four types

辛容量是研究辛拓扑和哈密尔顿动力系统的重要的不变量,对辛容量的计算和估计通常是很困难的.本文对多复变函数论和复几何中的一类重要的研究对象———典型域进行了Gromov辛宽度和Hofer-Zehnder辛容量的计算,并对四类典型域做出了较好的上、下界的估计,极大地方便了典型域的进一步研究.

The symplectic capacities are important invariant in the study of symplectic topology and Hamihonian dynam- ics. However, their computations and estimations are difficult. In this paper, we calculate and estimate the Gromov sym- plectic width and Hofer-Zehnder symplectic capacities of the classical domains of four types which play important roles in the theory of functions of several complex variables and complex geometry. This is very useful to the further study of the classi cal domains.