English

Mean Curvature Flows of Two-Convex Lagrangians

Differential Geometry 2023-12-22 v2

Abstract

We prove regularity, global existence, and convergence of Lagrangian mean curvature flows in the two-convex case. Such results were previously only known in the convex case, of which the current work represents a significant improvement. The proof relies on a newly discovered monotone quantity that controls two-convexity. Through a unitary transformation, same result for the mean curvature flow of area-decreasing Lagrangian submanifolds were established.

Keywords

Cite

@article{arxiv.2302.02512,
  title  = {Mean Curvature Flows of Two-Convex Lagrangians},
  author = {Chung-Jun Tsai and Mao-Pei Tsui and Mu-Tao Wang},
  journal= {arXiv preprint arXiv:2302.02512},
  year   = {2023}
}

Comments

typos corrected; small changes reflecting referee comments; to appear in J. Differential Geom