TL;DR
This survey reviews the theory of affine spheres, focusing on convex cases and their connections to Monge-Ampere equations and geometric structures on manifolds.
Contribution
It provides a comprehensive overview of affine spheres, highlighting recent developments and their relationships with important mathematical equations and structures.
Findings
Convex affine spheres are closely related to Monge-Ampere equations.
The survey summarizes key results and open problems in the field.
Connections to geometric structures on manifolds are emphasized.
Abstract
We give a survey of the theory of affine spheres, emphasizing the convex cases and relationsships to Monge-Ampere equations and geometric structures on manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory