The log-concavity of eigenfunction to complex Monge-Ampère operator in ℂ²

2025/05/19 by Wei Zhang, Qi Zhou, Zhang, Wei +1
#math.AP

paper · pdf · doi:10.48550/arxiv.2505.12817

Abstract

Following the authors' recent work \citeZhang-Zhou2025, we further explore the convexity properties of solutions to the Dirichlet problem for the complex Monge-Ampère operator. In this paper, we establish the log-concavity of solutions to the Dirichlet eigenvalue problem for the complex Monge-Ampère operator on bounded, smooth, strictly convex domain in ℂ². Our approach combines a constant rank theorem adapted to the study of real convexity in the complex setting with a deformation method.

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