Abstract
We are interested in surfaces with boundary satisfying a sixth order non-linear elliptic partial differential equation associated with extremal surfaces of the L2-norm of the gradient of the mean curvature. We show that such surfaces satis-fying so-called ‘flat boundary conditions’ and small L2-norm of the second fundamental form are necessarily planar.
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Acknowledgements
Research supported by the Australian Research Council DP150100375 and DP180100431. The authors also acknowledge Benjamin Maldon (University of Newcastle) for assistance with typesetting through the University of Newcastle Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA).
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McCoy, J., Wheeler, G. (2020). A Rigidity Theorem for Ideal Surfaces with Flat Boundary. In: de Gier, J., Praeger, C., Tao, T. (eds) 2018 MATRIX Annals. MATRIX Book Series, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-030-38230-8_19
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DOI: https://doi.org/10.1007/978-3-030-38230-8_19
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