Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 3

Special Issue in Honor of Duong H. Phong

Edited by Tristan Collins, Valentino Tosatti, and Ben Weinkove

Weak geodesics for the deformed Hermitian–Yang–Mills equation

Pages: 1113 – 1137

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n3.a12


Adam Jacob (University of California, Davis, Cal., U.S.A.)


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 $C^0$ solutions of the associated Dirichlet problem.

The author’s research was supported in part by a Simons Collaboration Grant.

Received 27 March 2019

Accepted 15 June 2019

Published 14 June 2021