Stability of solutions to complex Monge-Ampere flows
Vincent Guedj (IMT), Hoang Chinh Lu (UP11 UFR Sciences), Ahmed Zeriahi, (IMT)
TL;DR
This paper proves a stability result for solutions to complex Monge-Ampère equations on compact Kähler manifolds, including applications to the Kähler-Ricci flow, enhancing understanding of their behavior under perturbations.
Contribution
It introduces a new stability theorem for elliptic and parabolic complex Monge-Ampère equations on compact Kähler manifolds, with specific application to the Kähler-Ricci flow.
Findings
Stability results for complex Monge-Ampère equations
Application to Kähler-Ricci flow
Enhanced understanding of solution behavior
Abstract
We establish a stability result for elliptic and parabolic complex Monge-Amp{\`e}re equations on compact K{\"a}hler manifolds, which applies in particular to the K{\"a}hler-Ricci flow. Dedicated to Jean-Pierre Demailly on the occasion of his 60th birthday.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory