Geodesic
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

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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.

Classification : 32Q15, 32W20, 58D27, 58E11 
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/
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     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},
     year = {2003},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {4},
     mrnumber = {2040638},
     zbl = {1170.32312},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_4_617_0/}
}
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