On stability and the convergence of the Kähler-Ricci flow

Phong, Duong H.; Sturm, Jacob

J. Differential Geom., Tome 72 (2006) no. 1, p. 149-168 / Harvested from Project Euclid

Résumé

Assuming uniform bounds for the curvature, the exponential convergence of the Kähler-Ricci flow is established under two conditions which are a form of stability: the Mabuchi energy is bounded from below, and the dimension of the space of holomorphic vector fields in an orbit of the diffeomorphism group cannot jump up in the limit.

Publié le : 2006-01-14
Classification:

@article{1143593129,
     author = {Phong, Duong H. and Sturm, Jacob},
     title = {On stability and the convergence of the K\"ahler-Ricci flow},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 149-168},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1143593129}
}

Phong, Duong H.; Sturm, Jacob. On stability and the convergence of the Kähler-Ricci flow. J. Differential Geom., Tome 72 (2006) no. 1, pp.  149-168. http://gdmltest.u-ga.fr/item/1143593129/