Compactness and convexity results for closed relativistic strings
Mathematical Physics
2010-01-31 v2 math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.1001.4410,
title = {Compactness and convexity results for closed relativistic strings},
author = {G. Bellettini and J. Hoppe and M. Novaga and G. Orlandi},
journal= {arXiv preprint arXiv:1001.4410},
year = {2010}
}
Comments
22 pages, 2 figures