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arXiv:1703.00090 [math.DG]AbstractReferencesReviewsResources

Lagrangian Mean Curvature Flows and Moment maps

Hiroshi Konno

Published 2017-02-28Version 1

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 Euclid spaces. We also construct 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.

Comments: 34 pages, 1 figure
Categories: math.DG, math.SG
Subjects: 53C44, 53D12, 53D20
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