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Degenerate Complex Hessian Equations on Compact Kahler Manifolds

Hoang Chinh Lu (Institutionen för matematiska vetenskaper) ; V. D. Nguyen
Indiana University Mathematics Journal (0022-2518). Vol. 64 (2015), 6, p. 1721-1745.
[Artikel, övrig vetenskaplig]

Let (X, omega) be a compact Kahler manifold of dimension n, and fix m is an element of N such that 1 <= m <= n. We prove that any (omega, m)-subharmonic function can be approximated from above by smooth (omega, m)-subharmonic functions. A potential theory for the complex Hessian equation is also developed that generalizes the classical pluripotential theory on compact Kahler manifolds. We then use novel variational tools due to Berman, Boucksom, Guedj, and Zeriahi to solve degenerate complex Hessian equations.

Nyckelord: Complex Hessian, potential theory, variational method, regularization



Denna post skapades 2016-02-10.
CPL Pubid: 231902

 

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