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2021•Annales de l’institut FourierOpen access

Stability and Hölder regularity of solutions to complex Monge–Ampère equations on compact Hermitian manifolds

Chinh H. Lu, Trong-Thuc Phung, Tat Dat Tô

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Abstract

Let ( X , ω ) be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge–Ampère equations with right-hand side in L p , p > 1 . Using this we prove that the solutions are Hölder continuous with the same exponent as in the Kähler case by Demailly–Dinew–Guedj–Kołodziej–Pham–Zeriahi. Our techniques also apply to the setting of big cohomology classes on compact Kähler manifolds.

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Let ( X , ω ) be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge–Ampère equations with right-hand side in L p , p > 1 . Using this we prove that the solutions are Hölder continuous with the same exponent as in the Kähler case by Demailly–Dinew–Guedj–Kołodziej–Pham–Zeriahi. Our techniques also apply to the setting of big cohomology classes on compact Kähler manifolds.

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Available abstract

Let ( X , ω ) be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge–Ampère equations with right-hand side in L p , p > 1 . Using this we prove that the solutions are Hölder continuous with the same exponent as in the Kähler case by Demailly–Dinew–Guedj–Kołodziej–Pham–Zeriahi. Our techniques also apply to the setting of big cohomology classes on compact Kähler manifolds.

Key concepts: Hermitian matrix, Mathematics, Hermitian symmetric space, Pure mathematics, Kähler manifold, Manifold (fluid mechanics), Stability (learning theory), Hermitian manifold

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