Existence of Lagrangian Mean Curvature Flow Singularities with Bounded Mean Curvature
Abstract
In every dimension n ≥ 3, we show there exist Lagrangian mean curvature flows that develop neck pinch singularities such that the mean curvature remains uniformly bounded. This follows from a related result that, under a structural assumption on the singularity formation, the mean curvature at small scales near the singularity can be bounded by the Lagrangian angle at outer scales with suitable weights. Applying this result to a subset of the finite-time Lagrangian mean curvature flow singularities constructed in the companion paper [arXiv:2607.03152] and the infinite-time Lagrangian mean curvature flow singularities constructed by Tsai, Wood, and the second-named author [arXiv:2401.02228] then gives examples of both finite-time and infinite-time singularity formation with uniformly bounded mean curvature.
Related
- The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow
- Singularities of Mean Curvature Flow with Bounded Total Curvature
- Gradient estimates for the Lagrangian mean curvature equation with Lipschitz critical phase
- Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature
- Lagrangian mean curvature flow in the Kummer K3 surface
BibTeX
@misc{stolarski2026existence,
title = {{Existence of Lagrangian Mean Curvature Flow Singularities with Bounded Mean Curvature}},
author = {Maxwell Stolarski and Wei-Bo Su},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06248},
eprint = {2611.06248},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06248},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Existence of Lagrangian Mean Curvature Flow Singularities with Bounded Mean Curvature
AU - Maxwell Stolarski
AU - Wei-Bo Su
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06248
UR - https://arxiv.org/abs/2611.06248
AB - In every dimension n ≥ 3, we show there exist Lagrangian mean curvature flows that develop neck pinch singularities such that the mean curvature remains uniformly bounded. This follows from a related result that, under a structural assumption on the singularity formation, the mean curvature at small scales near the singularity can be bounded by the Lagrangian angle at outer scales with suitable weights. Applying this result to a subset of the finite-time Lagrangian mean curvature flow singularities constructed in the companion paper [arXiv:2607.03152] and the infinite-time Lagrangian mean curvature flow singularities constructed by Tsai, Wood, and the second-named author [arXiv:2401.02228] then gives examples of both finite-time and infinite-time singularity formation with uniformly bounded mean curvature.
ER -