English

Regularity for Hamiltonian stationary equations in $\mathbb{R}_{n\leq 4}^{n}$

Analysis of PDEs 2025-04-30 v1 Differential Geometry

Abstract

In this paper, we study the regularity of solutions to the Hamiltonian stationary equation in complex Euclidean space. We show that in dimensions n4n\leq 4, for all values of the Lagrangian phase, any C1,1C^{1,1} solution is smooth and derive a Ck,αC^{k,\alpha} estimate for it, where k2k \geq 2.

Keywords

Cite

@article{arxiv.2504.18013,
  title  = {Regularity for Hamiltonian stationary equations in $\mathbb{R}_{n\leq 4}^{n}$},
  author = {Arunima Bhattacharya},
  journal= {arXiv preprint arXiv:2504.18013},
  year   = {2025}
}