Abstract
In this paper, we prove the light-likeness of bordlines of smooth extremal surfaces of mixed type in general physical space-times, and for the case of the (1+2)-dimensional Minkowski space R1+2, we improve a Gu's theorem on the light-likeness of bordlines of extremal surfaces in R1+2. As a consequence, we show that a curve moving in a physical space-time keeps its like-property and the bordline only exists when its world sheet at the initial time has light-like points. This implies that any extremal surface of mixed type is generated by an \initial curve of mixed type".
Key words and phrases: Space-time, Extremal surface of mixed type, Bordline, Light-likeness.
2000 Mathematics Subject Classication: 35Q75, 35L70, 70H40.