Rigidity of entire self-shrinking solutions to K\"ahler-Ricci flow on complex plane
Wenlong Wang
TL;DR
This paper proves that all entire self-shrinking solutions to the K"ahler-Ricci flow on the complex plane are quadratic potentials, revealing a rigidity property of such solutions.
Contribution
It establishes a rigidity result showing that entire self-shrinking solutions are necessarily quadratic, a new characterization in the study of K"ahler-Ricci flow.
Findings
All entire self-shrinking solutions are quadratic potentials.
The result applies specifically to solutions on the complex plane.
It advances understanding of the structure of solutions to K"ahler-Ricci flow.
Abstract
We show that every entire self-shrinking solution on to the K\"ahler-Ricci flow must be generated from a quadratic potential.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Meromorphic and Entire Functions