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.
The Eigenvalue Problem for the Complex Hessian Operator on $m$-Pseudoconvex Manifolds
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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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An Iterative Approach to the Complex Monge-Amp\`ere Eigenvalue Problem
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.