The Eigenvalue Problem for the Complex Hessian Operator on $m$-Pseudoconvex Manifolds
Complex Variables
2024-02-06 v1 Analysis of PDEs
Differential Geometry
Abstract
We establish -regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly -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.
Cite
@article{arxiv.2402.03098,
title = {The Eigenvalue Problem for the Complex Hessian Operator on $m$-Pseudoconvex Manifolds},
author = {Jianchun Chu and Yaxiong Liu and Nicholas McCleerey},
journal= {arXiv preprint arXiv:2402.03098},
year = {2024}
}