三维Minkowski空间中的定态带
Stationary bands in three-dimensional Minkowski space
摘要：
本文考虑三维Lorentz-Minkowski空间$ł^3$中的自由边界问题，它涉及中曲率为时间坐标的线性函数且边界在给定支撑平面内移动的类空曲面。我们研究类空曲面，项目一对一到一条的支持，并在当地的临界点的某一能量功能涉及的表面，类时的潜力和保持封闭的表面的体积。我们称这些表面为固定带。我们建立存在这样的表面，我们调查他们的定性性质。最后，我们给出了它的大小估计的初始数据。
英文摘要：
In this paper we consider a free boundary problem in the 3-dimensional Lorentz-Minkowski space $ł^3$ which deals spacelike surfaces whose mean curvature is a linear function of the time coordinate and the boundary moves in a given support plane. We study spacelike surfaces that project one-to-one into a strip of the support and that locally are critical points of a certain energy functional involving the area of the surface, a timelike potential and preserves the volume enclosed by the surface. We call these surfaces stationary bands. We establish existence of such surfaces and we investigate their qualitative properties. Finally, we give estimates of its size in terms of the initial data.
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