Tohoku Mathematical Journal
2013
September
SECOND SERIES VOL. 65, NO. 3

Tohoku Math. J.
65 (2013), 411-425

Title SOME EXAMPLES OF SELF-SIMILAR SOLUTIONS AND TRANSLATING SOLITONS FOR LAGRANGIAN MEAN CURVATURE FLOW

Author Hiroshi Nakahara

(Received September 27, 2011, revised July 2, 2012)
Abstract. We construct examples of self-similar solutions and translating solitons for Lagrangian mean curvature flow by extending the method of Joyce, Lee and Tsui. Those examples include examples in which the Lagrangian angle is arbitrarily small as the examples of Joyce, Lee and Tsui. The examples are non-smooth zero-Maslov class Lagrangian self-expanders which are asymptotic to a pair of planes intersecting transversely.

Mathematics Subject Classification. Primary 53C44; Secondary 53D12.
Key words and phrases. Lagrangian mean curvature flow, self-similar solution, translating soliton.

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