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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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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description 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 .
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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
title Continuous Solutions to Complex Hessian Equations on Hermitian Manifolds
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