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In this paper we prove the existence of solutions of a degenerate complex Monge-Ampére equation on a complex manifold. Applying our existence result to a special degeneration of complex structure, we show how to associate to a change of complex structure an infinite length geodetic ray in the space of potentials. We also prove an existence result for the initial value problem for geodesics. We end this paper with a discussion of a list of open problems indicating how to relate our reults to the existence problem for extremal metrics.
@article{ASNSP_2003_5_2_4_617_0,
author = {Arezzo, Claudio and Tian, Gang},
title = {Infinite geodesic rays in the space of {K\"ahler} potentials},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {617--630},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 2},
number = {4},
year = {2003},
mrnumber = {2040638},
zbl = {1170.32312},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_617_0/}
}
TY - JOUR AU - Arezzo, Claudio AU - Tian, Gang TI - Infinite geodesic rays in the space of Kähler potentials JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 617 EP - 630 VL - 2 IS - 4 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_617_0/ LA - en ID - ASNSP_2003_5_2_4_617_0 ER -
%0 Journal Article %A Arezzo, Claudio %A Tian, Gang %T Infinite geodesic rays in the space of Kähler potentials %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 617-630 %V 2 %N 4 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_617_0/ %G en %F ASNSP_2003_5_2_4_617_0
Arezzo, Claudio; Tian, Gang. Infinite geodesic rays in the space of Kähler potentials. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 4, pp. 617-630. http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_617_0/