Infinite geodesic rays in the space of Kähler potentials

Claudio Arezzo; Gang Tian

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2003)

  • Volume: 2, Issue: 4, page 617-630
  • ISSN: 0391-173X

Abstract

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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.

How to cite

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Arezzo, Claudio, and Tian, Gang. "Infinite geodesic rays in the space of Kähler potentials." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 2.4 (2003): 617-630. <http://eudml.org/doc/84514>.

@article{Arezzo2003,
abstract = {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.},
author = {Arezzo, Claudio, Tian, Gang},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {617-630},
publisher = {Scuola normale superiore},
title = {Infinite geodesic rays in the space of Kähler potentials},
url = {http://eudml.org/doc/84514},
volume = {2},
year = {2003},
}

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
PB - Scuola normale superiore
VL - 2
IS - 4
SP - 617
EP - 630
AB - 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.
LA - eng
UR - http://eudml.org/doc/84514
ER -

References

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