Work

The Kähler-Ricci flow and the [symbol] operator on vector fields

Year: 2009

Type: article

Abstract: The limiting behavior of the normalized Kähler-Ricci flow for manifolds with positive first Chern class is examined under certain stability conditions.First, it is shown that if the Mabuchi Kenergy is bounded from below, then the scalar curvature converges uniformly to a constant.Second, it is shown that if the Mabuchi Kenergy is bounded from below and if the lowest positive eigenvalue of the ∂ † ∂ operator on smooth vector fields is bounded away from 0 along the flow, then the metrics converge exponentially fast in C ∞ to a Kähler-Einstein metric.

Source: Journal of Differential Geometry

DOI: 10.4310/jdg/1236604346

Authors: D.H. Phong, Jian Song, Jacob Sturm, Ben Weinkove

Institutions: Johns Hopkins University, Columbia University, Rutgers, The State University of New Jersey, Harvard University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: Canonical metrics and stability, Problems in Analysis at the Interface with Geometry and Physics, Parabolic flows and canonical metrics in Kahler geometry., Nonlinear Geo metric Equations of Monge-Ampere Type and Canonical Metrics