Year: 2026
Type: preprint
Abstract: In this paper, we investigate Hamiltonian stationary Lagrangian currents with single-valued phases in open sets of Ricci-flat Kähler manifolds. We first establish the relation between phase and mean curvature for a class of integral Lagrangian currents in Ricci-flat Kähler manifolds. Then we derive several fundamental properties of integral Lagrangian currents with single-valued harmonic phases, including an almost monotonicity formula, an Allard-type regularity theorem, and the structure of limits of currents in this class. Finally, we apply the above results to study the regularity and rigidity of Hamiltonian stationary Lagrangian graphs in complex Euclidean space under certain conditions.
Source: arXiv (Cornell University)
Author: Ding, Qi
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3221272539
OpenAlex ID: W7213329871