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math.AP2026
Second order estimates for equations with sums of Hessian operators on Hermitian manifolds
Weisong Dong, Ruijia Zhang
In this paper, we establish an a priori second-order estimate for admissible solutions satisfying a dynamic plurisubharmonic condition to equations involving sums of Hessian operat…
math.AP2026
Pogorelov interior estimates for general sum-type Hessian equations
Weisong Dong, Sirui Xu, Ruijia Zhang
In this paper, we exploit the concavity of sums of Hessian operators to derive Pogorelov estimates for corresponding equations under the dynamic semi-convexity assumption, and we f…
math.AP2025
estimates for -Hessian equations and a rigidity theorem
Ruijia Zhang
We derive a concavity inequality for -Hessian operators under the semi-convexity condition. As an application, we establish interior estimates for semi-convex solutions of the $…