Rigidity of complete entire self-shrinking solutions to Kahler-Ricci flow
Gregory Drugan, Peng Lu, Yu Yuan
TL;DR
This paper proves that all complete entire self-shrinking solutions to the Kahler-Ricci flow on complex Euclidean space are generated from quadratic potentials, revealing a rigidity property of such solutions.
Contribution
It establishes a rigidity result showing that these solutions must originate from quadratic potentials, a new characterization in Kahler-Ricci flow theory.
Findings
All solutions are quadratic potentials.
Complete entire solutions are uniquely characterized.
Supports the rigidity conjecture in Kahler-Ricci flow.
Abstract
We show that every complete entire self-shrinking solution on complex Euclidean space to the Kahler-Ricci flow must be generated from a quadratic potential.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Meromorphic and Entire Functions