Academics

Differential Geometry Seminar | The eigenvalue problem of complex Hessian operators

Time:Tues., 21:00-22:00, Mar. 19, 2024

Venue:Zoom Meeting ID: 271 534 5558 Passcode: YMSC

Organizer:Jialong Deng, Akito Futaki

Speaker:Yaxiong Liu (University of Maryland)

Abstract:

In a very recent pair of nice papers of Badiane and Zeriahi, they consider the eigenvalue problem of complex Monge-Ampere and complex Hessian, and show that the C^{1,\bar{1}}-regularity of eigenfunction for MA and C^alpha-regularity for complex Hessian. They posed a question about the C^{1,1}-regularity. We give a positive answer and show the C^{1,1}-regularity and uniqueness of the eigenfunction. We also derive a number of applications, including a bifurcation-type theorem and geometric bounds for the eigenvalue. This is a joint work with Jianchun Chu and Nicholas McCleerey.

DATEMarch 19, 2024
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