About the Calabi problem: a finite dimensional approach

Details About the Calabi problem: a finite dimensional approach About the Calabi problem: a finite dimensional approach

2011-02-05

arxiv.org/abs/1102.1097v2

Mathematics

Differential Geometry

38 pages. Revised version with improved exposition

Scientific paper

Let us consider a projective manifold and $\Omega$ a volume form. We define the gradient flow associated to the problem of $\Omega$-balanced metrics in the quantum formalism, the \Omega$-balacing flow. At the limit of the quantization, we prove that the $\Omega$-balacing flow converges towards a natural flow in K\"ahler geometry, the $\Omega$-K\"ahler flow. We study the existence of the $\Omega$-K\"ahler flow and proves its long time existence and convergence towards the solution to the Calabi problem of prescribing the volume form in a given K\"ahler class. We derive some natural geometric consequences of our study.

Affiliated with

Also associated with

No associations

Rating

About the Calabi problem: a finite dimensional approach 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 About the Calabi problem: a finite dimensional approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and About the Calabi problem: a finite dimensional approach will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-505794