4 papers · 1 filter
On a continuity method for Dirichlet problem of Hessian equations
Rirong Yuan
In this paper, we develop a continuity method for the Dirichlet problem of Hessian equations on Riemannian manifolds. Such equations, introduced by Caffarelli, Nirenberg and Spruck…
The structure of fully nonlinear equations and its applications to prescribed problems on complete conformal metrics
Rirong Yuan
This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and…
Fully non-linear elliptic equations on complex manifolds
Rirong Yuan
In this paper, we study a broad class of fully nonlinear elliptic equations on Hermitian manifolds. On one hand, under the optimal structural assumptions we derive -estim…
Fully nonlinear elliptic equations for some prescribed curvature problems on Hermitian manifolds
Rirong Yuan
We study fully nonlinear elliptic equations on Hermitian manifolds through blow-up argument and partial uniform ellipticity. We apply our results to draw geometric conclusions on f…