%0 Journal Article
%T Extremal metrics and K-stability (PhD thesis)
%A G¨˘bor Sz¨¦kelyhidi
%J Mathematics
%D 2006
%I arXiv
%X In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we conjecture to be equivalent to the existence of an extremal metric in the polarisation class. A variant for a complete extremal metric on the complement of a smooth divisor is also given. On toric surfaces we prove a Jordan-Holder type theorem for decomposing semistable surfaces into stable pieces. On a ruled surface we compute the infimum of the Calabi functional for the unstable polarisations, exhibiting a decomposition analogous to the Harder-Narasimhan filtration of an unstable vector bundle.
%U http://arxiv.org/abs/math/0611002v1