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The Eigenvalue Problem for the Complex Hessian Operator on $m$-Pseudoconvex Manifolds

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arxiv 2402.03098 v1 pith:MEMRNANA submitted 2024-02-05 math.CV math.APmath.DG

Jianchun Chu , Yaxiong Liu , Nicholas McCleerey This is my paper · ORCID
classification math.CVmath.APmath.DG
keywords eigenvaluecomplexfirsthessianmanifoldsoperatorpseudoconvexalong
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abstract

We establish $C^{1,1}$-regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly $m$-pseudoconvex manifolds, along with a variational formula for the first eigenvalue. From these results, we derive a number of applications, including a bifurcation-type theorem and geometric bounds for the eigenvalue.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A new approach to the Monge-Amp\`ere eigenvalue problem

    math.CV 2025-07 reject novelty 7.0 of 10

    For non-pluripolar measures on hyperconvex domains, the complex Monge-Ampère eigenvalue is unique, eigenfunctions are proportional, and the eigenvalue is the infimum of a Rayleigh quotient.

  2. An Iterative Approach to the Complex Monge-Amp\`ere Eigenvalue Problem

    math.CV 2025-07 accept novelty 6.0 of 10

    An inverse-iteration sequence converges uniformly to the eigenfunction of the complex Monge-Ampere Dirichlet eigenvalue problem, with Rayleigh quotients decreasing to the first eigenvalue.

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