The continuity equation on Hopf and Inoue surfaces
Xi Sisi Shen, Kevin Smith
TL;DR
This paper investigates the continuity equation on Hopf and Inoue surfaces, establishing a priori estimates and demonstrating Gromov-Hausdorff convergence of Inoue surfaces to a circle, advancing understanding in complex geometry.
Contribution
It extends the continuity equation analysis to Hermitian surfaces and proves convergence results, providing new insights into geometric structures on these surfaces.
Findings
A priori estimates for solutions on Hopf and Inoue surfaces
Gromov-Hausdorff convergence of Inoue surfaces to a circle
Extension of the continuity equation to Hermitian settings
Abstract
We study the continuity equation of La Nave-Tian, extended to the Hermitian setting by Sherman-Weinkove, on Hopf and Inoue surfaces. We prove a priori estimates for solutions in both cases, and Gromov-Hausdorff convergence of Inoue surfaces to a circle.
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Taxonomy
TopicsGeometry and complex manifolds · advanced mathematical theories · Algebraic Geometry and Number Theory