Symmetry Results for classical solutions of Monge-Ampere systems on a bounded planar domain
Li Ma, Baiyu Liu
TL;DR
This paper uses the method of moving planes to prove symmetry and monotonicity of convex solutions for Monge-Ampere systems on bounded planar domains, advancing understanding of their geometric properties.
Contribution
It establishes symmetry and monotonicity results for convex solutions of Monge-Ampere systems using the method of moving planes.
Findings
Convex solutions exhibit symmetry on bounded planar domains.
Monotonicity properties are confirmed for solutions.
Method of moving planes is effectively applied to Monge-Ampere systems.
Abstract
In this paper, by the method of moving planes, we establish the monotonicity and symmetry properties of convex solutions for Monge-Ampere systems on bounded smooth planar domains.
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
TopicsNonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows · Geometry and complex manifolds