Monge-Ampere type equations and their applications

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The study of Monge-Ampere equations has attracted major attention in mathematics in recent years, due to many significant applications in geometry, physics and applied science. This project aims to resolve challenging problems involving Monge-Ampere type equations, by utilising new ideas and breakthroughs made by the proposer. A comprehensive regularity theory for Monge-Ampere type equations, particularly in the degenerate case, is expected to be established. Innovative cutting-edge techniques and interdisciplinary approaches are expected to be developed. Anticipated outcomes of this project include the resolution of outstanding open problems and continuing enhancement of Australian leadership and expertise in a major area of mathematics.