Work

The interpolation method for the complex Hessian equation on compact Kähler manifolds

Year: 2026

Type: preprint

Abstract: In current work, we delve into the study of complex Hessian equations on compact Kähler manifolds. By imposing a constraint on both the bisectional curvature and the oscillation of the solution, we demonstrate that the Laplacian estimate can be linearly controlled by its gradient estimate. Consequently, we are able to derive gradient estimate for the solution using a standard interpolation argument, without the need to employ the blow-up technique. As an application, we demonstrate that when the right-hand side of the complex Hessian equations approximate 1 in the $L^1$ norm, the desired gradient estimate is obtained.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.07852

Authors: Zhang, Jiaogen, Zhang, Xi

Institutions: Hefei University of Technology, Nanjing University of Science and Technology

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Natural Science Foundation of China, Hefei University of Technology

Awards: G1231468753, G222581545, G5123990054, G7197553430

OpenAlex ID: W7221015209

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