Search: onr:"swepub:oai:gup.ub.gu.se/207055" >
Real Monge-Ampere e...
Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
-
- Berman, Robert, 1976 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
-
- Berndtsson, Bo, 1950 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
-
(creator_code:org_t)
- 2014-01-22
- 2013
- English.
-
In: Annales de la faculté des sciences de Toulouse. - : Cellule MathDoc/CEDRAM. - 0240-2963 .- 2258-7519. ; 22:4, s. 649-711
- Related links:
-
http://arxiv.org/pdf...
-
show more...
-
http://dx.doi.org/10...
-
https://gup.ub.gu.se...
-
https://doi.org/10.5...
-
https://research.cha...
-
show less...
Abstract
Subject headings
Close
- We show, using a direct variational approach, that the second boundary value problem for the Monge-Ampère equation in $\mathbb{R}^{n}$ with exponential non-linearity and target a convex body $P$ is solvable iff $0$ is the barycenter of $P.$ Combined with some toric geometry this confirms, in particular, the (generalized) Yau-Tian-Donaldson conjecture for toric log Fano varieties $(X,\Delta )$ saying that $(X,\Delta )$ admits a (singular) Kähler-Einstein metric iff it is K-stable in the algebro-geometric sense. We thus obtain a new proof and extend to the log Fano setting the seminal result of Wang-Zhou concerning the case when $X$ is smooth and $\Delta $ is trivial. Li’s toric formula for the greatest lower bound on the Ricci curvature is also generalized. More generally, we obtain Kähler-Ricci solitons on any log Fano variety and show that they appear as the large time limit of the Kähler-Ricci flow. Furthermore, using duality, we also confirm a conjecture of Donaldson concerning solutions to Abreu’s boundary value problem on the convex body $P$ in the case of a given canonical measure on the boundary of $P.$
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
Find in a library
To the university's database