Pointing out a crucial relation with caustics of the eikonal equation we discuss the singularity formation of 2-dimensional surfaces that sweep out 3-manifolds of zero mean curvature in R3,1.
@article{bwmeta1.element.doi-10_1515_geofl-2015-0003, author = {J. Eggers and J. Hoppe and M. Hynek and N. Suramlishvili}, title = {Singularities of relativistic membranes}, journal = {Geometric Flows}, volume = {1}, year = {2015}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_geofl-2015-0003} }
J. Eggers; J. Hoppe; M. Hynek; N. Suramlishvili. Singularities of relativistic membranes. Geometric Flows, Tome 1 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_geofl-2015-0003/
[1] V. I. Arnol’d, V. A. Vasil’ev, V. V. Goryunov, and O. V. Lyashko, in Dynamical Syatems VIII (Springer, Heidelberg, 1993).
[2] G. Bellettini, J. Hoppe, M. Novaga, G. Orlandi, Complex Anal. Operator Theory 4, 3 (2010).
[3] J. Eggers and M.A. Fontelos, The role of self-similarity in singularities of partial differential equations, Nonlinearity 22, R1 (2009). [WoS][Crossref] | Zbl 1152.35300
[4] J. Eggers and J. Hoppe, Phys. Lett. B 680, 274 (2009).
[5] J. Hoppe, in Nonlinear Waves, Gakuto International Series: Mathematical Sciences and Applications, Vol. 8 (Gakkotosho, Tokyo, 1996), URL http://arxiv:hep-th/9503069.
[6] J. Hoppe, J. Phys. A: Math. Theor. 46, 023001 (2013). [Crossref]
[7] J. Nye, Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations (Institute of Physics Publishing, Bristol, 1999). | Zbl 0984.78002
[8] L. Nguyen and G. Tian, Class. Quantum Grav. 30, 16 (2013).
[9] Y. Pomeau, M. Le Berre, P. Guyenne, and S. Grilli, Nonlinearity 21, T61 (2008). [Crossref]
[10] N. Turok, Nucl. Phys B 242, 520 (1984).