Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915071769182208 |
|---|---|
| author | Lotay, Jason D. Oliveira, Goncalo |
| author_facet | Lotay, Jason D. Oliveira, Goncalo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05744 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry Lotay, Jason D. Oliveira, Goncalo Differential Geometry Analysis of PDEs Symplectic Geometry 53E10, 53C38, 53C26 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. |
| title | Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry |
| topic | Differential Geometry Analysis of PDEs Symplectic Geometry 53E10, 53C38, 53C26 |
| url | https://arxiv.org/abs/2305.05744 |