A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations
Analysis of PDEs
2015-05-18 v1
Abstract
Using an rotation of Yuan, we observe that the gradient graph of any semiconvex function is a Liouville manifold, that is, does not admit bounded harmonic functions. As a corollary, we find that any entire solution of the fourth order Hamiltonian stationary equation with Lagrangian phase angle uniformly larger than the critical angle must be a quadratic.
Keywords
Cite
@article{arxiv.1505.04152,
title = {A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations},
author = {Micah Warren},
journal= {arXiv preprint arXiv:1505.04152},
year = {2015}
}