The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds

Details The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds

2011-09-07

arxiv.org/abs/1109.1550v1

Mathematics

Differential Geometry

40 pages

Scientific paper

We study the Yang-Mills flow on a holomorphic vector bundle E over a compact Kahler manifold X . Along a solution of the flow, we show the trace of the curvature \Lambda F(A_t) approaches in L^2 an endomorphism with constant eigenvalues given by the slopes of the quotients from the Harder-Narasimhan filtration of E. This proves a sharp lower bound for the Hermitian-Yang-Mills functional and thus the Yang-Mills functional, generalizing to arbitrary dimension a formula of Atiyah and Bott first proven on Riemann surfaces. Furthermore, we show any reflexive extension to all of X of the limiting bundle E_\infty is isomorphic to Gr(E)^\star\star, verifying a conjecture of Bando and Siu.

Affiliated with

Also associated with

No associations

Rating

The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-306944