Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane

Details Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane Translating solitons for Lagrangian mean curvature flow in complex Euclidean plane

2010-07-12

arxiv.org/abs/1007.1886v1

Mathematics

Differential Geometry

15 pages

Scientific paper

Using certain solutions of the curve shortening flow, including self-shrinking and self-expanding curves or spirals, we construct and characterize many new examples of translating solitons for mean curvature flow in complex Euclidean plane. They generalize the Joyce, Lee and Tsui ones \cite{JLT} in dimension two. The simplest (non trivial) example in our family is characterized as the only (non totally geodesic) Hamiltonian stationary Lagrangian translating soliton for mean curvature flow in complex Euclidean plane.

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