Stability estimates for the complex Monge-Ampère and Hessian equations

Bin Guo; Duong H. Phong; Freid Tong

doi:10.1007/s00526-022-02344-y

Stability estimates for the complex Monge-Ampère and Hessian equations

Bin Guo, Duong H. Phong, Freid Tong

Rutgers Newark, Math & Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

A new proof for stability estimates for the complex Monge-Ampère and Hessian equations is given, which does not require pluripotential theory. A major advantage is that the resulting stability estimates are then uniform under general degenerations of the background metric in the case of the Monge-Ampère equation, and under degenerations to a big class in the case of Hessian equations.

Original language	English (US)
Article number	7
Journal	Calculus of Variations and Partial Differential Equations
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/s00526-022-02344-y
State	Published - Jan 2023

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00526-022-02344-y

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abstract = "A new proof for stability estimates for the complex Monge-Amp{\`e}re and Hessian equations is given, which does not require pluripotential theory. A major advantage is that the resulting stability estimates are then uniform under general degenerations of the background metric in the case of the Monge-Amp{\`e}re equation, and under degenerations to a big class in the case of Hessian equations.",

author = "Bin Guo and Phong, {Duong H.} and Freid Tong",

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N2 - A new proof for stability estimates for the complex Monge-Ampère and Hessian equations is given, which does not require pluripotential theory. A major advantage is that the resulting stability estimates are then uniform under general degenerations of the background metric in the case of the Monge-Ampère equation, and under degenerations to a big class in the case of Hessian equations.

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Stability estimates for the complex Monge-Ampère and Hessian equations

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