Z. Sui

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20242026

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math.AP2026

Interior Hessian estimates for Hessian quotient equations in dimension three

Heming Jiao, Zhenan Sui

In this paper, we establish the interior Hessian estimates for $2$ -convex solutions to $\frac{I ¨ _{2}}{I ¨ _{1}} (D^{2} u) = I ¨ (x, u)$ in dimension three. In higher dimensions ( $n \geq 4$ ),…

math.AP2025

Existence of solution to modified Gursky-Streets equation

Yi Huang, Zhenan Sui, Mingyu Xie

We solve the modified Gursky-Streets equation, which is a fully nonlinear equation arising in conformal geometry with uniform $C^{1, 1}$ estimates when (i) $I^^{3} > 0$ and $1 \leq k \l…

math.AP2025

Weak solutions to Hessian type equations on compact Riemannian manifolds

Zhenan Sui, Wei Sun

In this paper, we shall study the existence of weak solutions to Hessian type equations on compact Riemannian manifolds without boundary.