A Liouville's theorem for some Monge-Amp\`ere type equations
Hao Fang, Biao Ma, Wei Wei
TL;DR
This paper investigates a specific Monge-Ampère type equation that bridges the classical _2-Yamabe problem and the 2-Hessian equation in four dimensions, providing new insights into their mathematical structure.
Contribution
It introduces a Liouville's theorem for this class of Monge-Ampère equations, extending understanding of their solutions and properties.
Findings
Established a Liouville-type theorem for the equation
Connected the equation to classical geometric problems
Provided new analytical tools for Monge-Ampère equations
Abstract
We study a Monge-Amp\`ere type equation that interpolates the classical {\sigma_2} -Yamabe equation in conformal geometry and the 2-Hessian equation in dimension 4.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics