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The Eigenvalue Problem for the Complex Hessian Operator on $m$-Pseudoconvex Manifolds (2402.03098v1)
Published 5 Feb 2024 in math.CV, math.AP, and math.DG
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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