Heisenberg群上的Brouwer型不动点定理

The Brouwer-type Fixed Point Theorem on the Heisenberg Group

将欧式空间中经典的Brouwer不动点定理推广到了Heisenberg群H^n上,主要定理可叙述为:设f:B_H→B_H∩H_ξ是光滑映射,则f在B_H∩H_ξ中必有不动点,其中B_H为H^n中的单位闭球,H_ξ是过ξ∈B_H的水平平面.

In this paper,the classical Brouwer fixed point theorem in Euclidean space is generalized to the Henberg group Hn.The main result is as follows：If f：BH→BH∩Hξ is a smooth mapping,there exists a fixed point in BH∩Hξ,where Bn is a Koranyi unit closed ball,and Hξ is a horizontal plane through a point ξ∈BH.