CPL - Chalmers Publication Library
| Utbildning | Forskning | Styrkeområden | Om Chalmers | In English In English Ej inloggad.

Analytic torsion, vortices and positive Ricci curvature

Robert Berman (Institutionen för matematiska vetenskaper, matematik)
preprint på arxiv.org (2010)
[Artikel, övrig vetenskaplig]

We characterize the global maximizers of a certain non-local functional defined on the space of all positively curved metrics on an ample line bundle L over a Kahler manifold X. This functional is an adjoint version, introduced by Berndtsson, of Donaldson's L-functional and generalizes the Ding-Tian functional whose critical points are Kahler-Einstein metrics of positive Ricci curvature. Applications to (1) analytic torsions on Fano manifolds (2) Chern-Simons-Higgs vortices on tori and (3) Kahler geometry are given. In particular, proofs of conjectures of (1) Gillet-Soul\'e and Fang (concerning the regularized determinant of Dolbeault Laplacians on the two-sphere) (2) Tarantello and (3) Aubin (concerning Moser-Trudinger type inequalities) in these three settings are obtained. New proofs of some results in Kahler geometry are also obtained, including a lower bound on Mabuchi's K-energy and the uniqueness result for Kahler-Einstein metrics on Fano manifolds of Bando-Mabuchi. This paper is a substantially extended version of the preprint arXiv:0905.4263 which it supersedes.



Denna post skapades 2012-02-09.
CPL Pubid: 154961

 

Läs direkt!


Länk till annan sajt (kan kräva inloggning)


Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur