PreprintCC BY 4.0arXiv
Lagrangian mean curvature flow in the Kummer K3 surface
Abstract
A major problem in geometric analysis is to understand the behaviour of the Lagrangian mean curvature flow. This has proved to be a challenging problem, in particular, not many explicit examples of flows that exist for all time and converge to a minimal Lagrangian are known. In this paper we construct new examples of Lagrangian mean curvature flows in the Kummer K3 surface that converge to special Lagrangian spheres. We reduce the construction to a scalar perturbation problem that can be solved by a fixed point argument.
Related
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- Singularities of Mean Curvature Flow with Bounded Total Curvature
BibTeX
@misc{flores2026lagrangian,
title = {{Lagrangian mean curvature flow in the Kummer K3 surface}},
author = {Carlos Alberto Ochoa Flores},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34923},
eprint = {2609.34923},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34923},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lagrangian mean curvature flow in the Kummer K3 surface
AU - Carlos Alberto Ochoa Flores
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34923
UR - https://arxiv.org/abs/2609.34923
AB - A major problem in geometric analysis is to understand the behaviour of the Lagrangian mean curvature flow. This has proved to be a challenging problem, in particular, not many explicit examples of flows that exist for all time and converge to a minimal Lagrangian are known. In this paper we construct new examples of Lagrangian mean curvature flows in the Kummer K3 surface that converge to special Lagrangian spheres. We reduce the construction to a scalar perturbation problem that can be solved by a fixed point argument.
ER -