Scalar V-soliton equation and Kähler-Ricci flow on symplectic quotients

2020/01/29 by Chang Li, Li, Chang
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2001.11343

openalex publication_date 2020/01/29 · openalex created_date 2020/02/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the V-soliton equation which is a degenerate fully nonlinear equation introduced by La Nave and Tian in their work on Kähler-Ricci flow on symplectic quotients. One can apply the interpretation to study finite time singularities of the Kähler-Ricci flow. As in the case of Kähler-Einstein metrics, we can also reduce the V-soliton equation to a scalar equation on Kähler potentials, which is of Monge-Ampère type. We formulate some preliminary estimates for such a scalar equation on a compact Kähler manifold M.

Citations

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

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