Compactness and convexity results for closed relativistic strings

Details Compactness and convexity results for closed relativistic strings Compactness and convexity results for closed relativistic strings

2010-01-25

arxiv.org/abs/1001.4410v2

Physics

Mathematical Physics

22 pages, 2 figures

Scientific paper

We study various properties of closed relativistic strings. In particular, we characterize their closure under uniform convergence, extending a previous result by Y. Brenier on graph-like unbounded strings, and we discuss some related examples. Then we study the collapsing profile of convex planar strings which start with zero initial velocity, and we obtain a result analogous to the well-known theorem of Gage and Hamilton for the curvature flow of plane curves. We conclude the paper with the discussion of an example of weak Lipschitz evolution starting from the square in the plane, which exhibits some unexpected features.

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