Calculus of Variations and Geometric Measure Theory
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G. Bellettini - J. Hoppe - M. Novaga - G. Orlandi

Closure and convexity properties of closed relativistic strings

created by novaga on 28 Dec 2009
modified by orlandi on 09 Jan 2011


Published Paper

Inserted: 28 dec 2009
Last Updated: 9 jan 2011

Journal: Complex Analysis and Operator Theory
Volume: 4
Number: 3
Pages: 473-496
Year: 2010


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.


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