Curvature estimates for a class of Hessian type equations

Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

“…In this section, we will use an idea (which is similar to that in [7,9]) to give the proof of Theorem 1.1.…”

“…In 2020, Chu and Jiao [9] considered the Hessian type equation with vanishing Dirichlet boundary condition (DBC for short)…”

The Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds

“…If the complex Hessian matrix is replaced by the real Hessian matrix in (1.2), a natural question is whether we can study the regularity and solvability to the Dirichlet boundary problem for this kind of fully nonlinear equation (such as (1.1)). This work is a further study on the Dirichlet problem for (1.1) with gradient terms on the right sides of the equation following a recent work by Chu-Jiao [3]. To ensure the ellipticity of (1.1), we need λ[U] ∈ Γ k .…”

“…η ij is nonnegative definite) has been studied intensively by Sha [27,28], Wu [37], and Harvey-Lawson [16]. Recently, Chu-Jiao [3] considered the following prescribed curvature problem…”

Curvature estimates for $p$-convex hypersurfaces of prescribed curvature

“…For general curvature equations, see Caffarelli-Nirenberg-Spruck [4] and Gerhardt [11]. When p = n − 1, the equation was studied by Chu-Jiao [7] and, in complex settings, it is related to the Gauduchon conjecture which was solved by Székelyhidi-Tosatti-Weinkove [28]. For some previous work on this topic, see Tosatti-Weinkove [31,32] and Fu-Wang-Wu [9,10].…”