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