A minimizing deformation of Legendrian submanifolds in the standard sphere |
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Authors: | Hông-Vân Lê |
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Institution: | a Max-Planck-Institute for Mathematics in Sciences, Inselstraße 22-26, D-04103 Leipzig, Germany b Hanoi Institute of Mathematics, PO Box 10000 Boho, Hanoi, Viet Nam |
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Abstract: | In this note we study the moduli space of minimal Legendrian submanifolds in the standard sphere S2n−1. We show that new examples of minimal Legendrian submanifolds can be constructed, if we can solve a certain equation for a function on a nearby glued Legendrian submanifold. As a step toward solving this equation, we prove short-time existence for a particular gradient flow on the space of immersed Legendrian submanifolds. A new necessary condition for a Lagrangian embedding into is given. |
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Keywords: | 58G11 53D10 |
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