Construction of Lagrangian Self-similar Solutions to the Mean Curvature Flow inmathbb{C}^n |
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Authors: | Henri Anciaux |
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Affiliation: | (1) PUC-Rio, Rua Marques de Sao Vicente, 225 Gavea 22453-900, Rio de Janeiro, RJ, Brasil |
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Abstract: | We give new examples of self-shrinking and self-expanding Lagrangian solutions to the Mean Curvature Flow (MCF). These are Lagrangian submanifolds in , which are foliated by (n − 1)-spheres (or more generally by minimal (n − 1)-Legendrian submanifolds of ), and for which the study of the self-similar equation reduces to solving a non-linear Ordinary Differential Equation (ODE). In the self-shrinking case, we get a family of submanifolds generalising in some sense the self-shrinking curves found by Abresch and Langer. |
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Keywords: | Mean curvature flow Lagrangian submanifolds Self-similar |
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