A Lie algebraic approach to Ricci flow invariant curvature conditions and Harnack inequalities

By Burkhard Wilking. 2010

61 citations recorded by the source corpus.

Abstract We consider a subset S of the complex Lie algebra 𝔰𝔬(n, ℂ) and the cone C(S) of curvature operators which are nonnegative on S. We show that C(S) defines a Ricci flow invariant curvature condition if S is invariant under AdSO(n, ℂ). The analogue for Kähler curvature operators holds as well. Although the proof is very simple and short, it recovers all previously known invariant nonnegativity conditions. As an application we reprove that a compact Kähler manifold with positive orthogonal bisectional curvature evolves to a manifold with positive bisectional curvature and is thus biholomorphic to ℂℙn. Moreover, the methods can also be applied to prove Harnack inequalities.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/dffee8b9d6d7f3a851c33f9c30bfb7632fe03ba9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Ricci flow with surgery on manifolds with positive isotropic curvature (2017, unknown): “4 in [5] (see also [36]): Proposition A.”
How to produce a Ricci Flow via Cheeger-Gromoll exhaustion (2011, background): “Proposition 9] (see also the Appendix of [47]).”