Weak Geodesics for the deformed Hermitian-Yang-Mills equation
Differential Geometry
2019-06-18 v1 Analysis of PDEs
Abstract
We study weak geodesics in the space of potentials for the deformed Hermitian-Yang-Mills equation. The geodesic equation can be formulated as a degenerate elliptic equation, allowing us to employ nonlinear Dirichlet duality theory, as developed by Harvey-Lawson. By exploiting the convexity of the level sets of the Lagrangian angle operator in the highest branch, we are able to construct continuous solutions of the associated Dirichlet problem.
Keywords
Cite
@article{arxiv.1906.07128,
title = {Weak Geodesics for the deformed Hermitian-Yang-Mills equation},
author = {Adam Jacob},
journal= {arXiv preprint arXiv:1906.07128},
year = {2019}
}
Comments
Final version to appear in Pure and Applied Mathematics Quarterly