Abstract
This paper aims to establish the well-posedness on time interval \([0,\varepsilon ^{-\frac{1}{2}}T]\) of the classical initial problem for the bosonic membrane in the light cone gauge. Here \(\varepsilon \) is the small parameter which measures the nonlinear effects. The bosonic membrane is timelike submanifolds with vanishing mean curvature. Since the initial Riemannian metric may be degenerate, the corresponding equation can be reduced to a quasi-linear degenerate hyperbolic system of second order with an area preserving constraint via a Hamiltonian reduction.
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Acknowledgements
The first author expresses his sincere thanks to Prof G. Tian for introducing him to the subject of minimal surface and his many discussions, and his sincere thanks to Prof Q. Han for his discussion on Nash–Moser iteration scheme, and thanks to Prof S.J. Huang for his interest on this problem and some discussions. The first author is supported by NSFC (No. 11771359), and the Fundamental Research Funds for the Central Universities (Nos. 20720190070 and 20720180009). The second author is supported by NSFC (No. 11871199).
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Yan, W., Zhang, B. Long Time Existence for the Bosonic Membrane in the Light Cone Gauge. J Geom Anal 31, 395–422 (2021). https://doi.org/10.1007/s12220-019-00269-1
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DOI: https://doi.org/10.1007/s12220-019-00269-1