Relative Chow stability and extremal metrics
Reza Seyyedali
TL;DR
This paper establishes that the existence of extremal metrics on polarized manifolds implies a form of stability called asymptotic relative Chow stability, leading to uniqueness results for these metrics.
Contribution
It proves that extremal metrics imply asymptotic relative Chow stability and demonstrates the uniqueness of extremal metrics up to automorphisms.
Findings
Existence of extremal metrics implies asymptotic relative Chow stability.
Extremal metrics are unique up to automorphisms in any polarization.
Abstract
We prove that the existence of extremal metrics implies asymptotically relative Chow stability. An application of this is the uniqueness, up to automorphisms, of extremal metrics in any polarization.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Holomorphic and Operator Theory