Continuous Solutions to Complex Hessian Equations on Hermitian Manifolds

In this paper, we study and discuss existence and continuity of solution to complex Hessian equation ( χ + d d c · ) k ∧ ω n - k = c f ω n on Hermitian manifold ( X , ω ) , where χ is some smooth real ( 1 , 1 ) - form in X and Hermitian form ω satisfies that at every given point on X , there exist a...

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Bibliographic Details
Published in:The Journal of geometric analysis 2023-12, Vol.33 (12), Article 368
Main Authors: Hai, Le Mau, Van Quan, Vu
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Manifolds
Mathematics
Mathematics and Statistics
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Summary:In this paper, we study and discuss existence and continuity of solution to complex Hessian equation ( χ + d d c · ) k ∧ ω n - k = c f ω n on Hermitian manifold ( X , ω ) , where χ is some smooth real ( 1 , 1 ) - form in X and Hermitian form ω satisfies that at every given point on X , there exist a local chart Ω and a smooth real-valued function G such that e G ω is a Kähler form on Ω .
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01431-6