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arXiv · 1703.00090

Lagrangian Mean Curvature Flows and Moment maps

Hiroshi Konno
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Abstract

In this paper, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclidean spaces. Moreover, our method can be applied to construct examples of Lagrangian mean curvature flows in non-flat Calabi-Yau manifolds. In particular, we describe Lagrangian mean curvature flows in 4-dimensional Ricci-flat ALE spaces in detail and investigate their singularities.

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Hiroshi Konno. 2017-02-28. Lagrangian Mean Curvature Flows and Moment maps. https://arxiv.org/abs/1703.00090

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