Pure and Applied Mathematics Quarterly

Volume 15 (2019)

Number 4

Special Issue in Honor of Simon Donaldson: Part 2 of 2

Guest Editor: Richard Thomas (Imperial College London)

A class of fully nonlinear equations

Pages: 1029 – 1045

DOI: https://dx.doi.org/10.4310/PAMQ.2019.v15.n4.a3


Xiuxiong Chen (Stony Brook University, Stony Brook, New York, U.S.A.)

Weiyong He (University of Oregon, Eugene, Oregon, U.S.A.)


In this paper we consider a class of fully nonlinear equations which covers the equation introduced by S. Donaldson a decade ago and the equation introduced by Gursky–Streets recently. We solve the equation with uniform weak $C^2$ estimates, which hold for degenerate case.


fully nonlinear equations, a priori estimates

2010 Mathematics Subject Classification


The first author is supported in part by an NSF fund. The second author is supported partly by an NSF fund, award no. 1611797.

Received 30 November 2017

Published 20 March 2020