5 citations · 9 across the 19 of their papers we have counts for
19 papers
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 existence of negatively curved metrics on locally conformally flat manifolds with boundary
Rirong Yuan
We use certain Morse functions to construct conformal metrics with negative sectional curvature on locally conformally flat manifolds with boundary. Moreover, without conformally f…
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 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…
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 -estima…
Notes on conformal metrics of negative curvature on manifolds with boundary
Rirong Yuan
We use certain Morse functions to construct conformal metrics such that the eigenvalue vector of modified Schouten tensor belongs to a given cone. As a result, we prove that any Ri…
An extension of prescribed problems on the conformal classes of complete metrics
Rirong Yuan
We solve prescribed problems for modified Schouten tensors in the conformal classes of smooth complete metrics, which extends the results obtained in prequel \cite{yuan-PUE1}. The…
On the conformal bending of a closed Riemannian manifold
Rirong Yuan
In this paper, we bend a closed Riemannian manifold in the conformal class, through solving a fully nonlinear equation. As a result, we prove that each metric of quasi-negative Ric…
The Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds
Rirong Yuan
We derive the existence of -solutions to the Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds under appropriate assumptions.
On the level set version of partial uniform ellipticity and applications
Rirong Yuan
We derive level set version of partial uniform ellipticity for symmetric concave functions. This suggests an effective approach to investigate second order fully nonlinear equation…
The Dirichlet problem for Monge-Ampère equation for -PSH functions on Hermitian manifolds
Rirong Yuan
We solve the Dirichlet problem for Monge-Ampère equation for -PSH functions possibly with degenerate right-hand side, through deriving a quantitative version of boundary est…
On the regularity of Dirichlet problem for fully non-linear elliptic equations on Hermitian manifolds
Rirong Yuan
We derive the solvability and regularity of the Dirichlet problem for fully non-linear elliptic equations possibly with degenerate right-hand side on Hermitian manifolds, through e…
Regularity of fully non-linear elliptic equations on Hermitian manifolds
Rirong Yuan
In this paper we propose new insights and ideas to set up quantitative boundary estimates for solutions to Dirichlet problem of a class of fully non-linear elliptic equations on co…
The partial uniform ellipticity and prescribed problems on the conformal classes of complete metrics
Rirong Yuan
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effect…
Regularity of fully non-linear elliptic equations on Hermitian manifolds. III
Rirong Yuan
Under structural conditions which are almost optimal, we derive a quantitative version of boundary estimate then prove existence of solutions to Dirichlet problem for a class of fu…
Local -estimate and existence theorems for some prescribed curvature problems on complete noncompact Riemannian manifolds
Rirong Yuan
In this article we study a class of prescribed curvature problems on complete noncompact Riemannian manifolds. To be precise, we derive local -estimate under an asymptotic con…
On the partial uniform ellipticity and complete conformal metrics with prescribed curvature functions on manifolds with boundary
Rirong Yuan
We consider the problem of finding complete conformal metrics with prescribed curvature functions of the Einstein tensor and of more general modified Schouten tensors. To achieve t…
The Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with mean concave boundary
Rirong Yuan
This article studies the Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with \textit{mean concave} boundary in the sense tha…
Regularity of fully non-linear elliptic equations on Hermitian manifolds. II
Rirong Yuan
In this paper we investigate the regularity and solvability of solutions to Dirichlet problem for fully non-linear elliptic equations with gradient terms on Hermitian manifolds, wh…