Paper · May 9, 2023
Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry
As on arXiv
Abstract
In this article we consider the Lagrangian mean curvature flow of compact, circle-invariant, almost calibrated Lagrangian surfaces in hyperkähler 4-manifolds with circle symmetry. We show that this Lagrangian mean curvature flow can be continued for all time, through finite time singularities, and converges to a chain of special Lagrangians, thus verifying various aspects of Joyce's conjectures in this setting. We show that the singularities of the flow are neck pinches in the sense conjectured by Joyce. We also give examples where such finite time singularities are guaranteed to occur.
Comments: 27 pages, 6 figures; changes to proofs of Propositions 3.4 and 4.2, plus other minor changes, accepted in JEMS
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
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