Monge-Ampère Equations, Geodesics and Geometric Invariant Theory

D.H. Phong[1]; Jacob Sturm[2]

  • [1] Department of Mathematics Columbia University, New York, NY 10027
  • [2] Department of Mathematics Rutgers University, Newark, NJ 07102

Journées Équations aux dérivées partielles (2005)

  • page 1-15
  • ISSN: 0752-0360

Abstract

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Existence and uniqueness theorems for weak solutions of a complex Monge-Ampère equation are established, extending the Bedford-Taylor pluripotential theory. As a consequence, using the Tian-Yau-Zelditch theorem, it is shown that geodesics in the space of Kähler potentials can be approximated by geodesics in the spaces of Bergman metrics. Motivation from Donaldson’s program on constant scalar curvature metrics and Yau’s strategy of approximating Kähler metrics by Bergman metrics is also discussed.

How to cite

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Phong, D.H., and Sturm, Jacob. "Monge-Ampère Equations, Geodesics and Geometric Invariant Theory." Journées Équations aux dérivées partielles (2005): 1-15. <http://eudml.org/doc/10602>.

@article{Phong2005,
abstract = {Existence and uniqueness theorems for weak solutions of a complex Monge-Ampère equation are established, extending the Bedford-Taylor pluripotential theory. As a consequence, using the Tian-Yau-Zelditch theorem, it is shown that geodesics in the space of Kähler potentials can be approximated by geodesics in the spaces of Bergman metrics. Motivation from Donaldson’s program on constant scalar curvature metrics and Yau’s strategy of approximating Kähler metrics by Bergman metrics is also discussed.},
affiliation = {Department of Mathematics Columbia University, New York, NY 10027; Department of Mathematics Rutgers University, Newark, NJ 07102},
author = {Phong, D.H., Sturm, Jacob},
journal = {Journées Équations aux dérivées partielles},
language = {eng},
month = {6},
pages = {1-15},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Monge-Ampère Equations, Geodesics and Geometric Invariant Theory},
url = {http://eudml.org/doc/10602},
year = {2005},
}

TY - JOUR
AU - Phong, D.H.
AU - Sturm, Jacob
TI - Monge-Ampère Equations, Geodesics and Geometric Invariant Theory
JO - Journées Équations aux dérivées partielles
DA - 2005/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 15
AB - Existence and uniqueness theorems for weak solutions of a complex Monge-Ampère equation are established, extending the Bedford-Taylor pluripotential theory. As a consequence, using the Tian-Yau-Zelditch theorem, it is shown that geodesics in the space of Kähler potentials can be approximated by geodesics in the spaces of Bergman metrics. Motivation from Donaldson’s program on constant scalar curvature metrics and Yau’s strategy of approximating Kähler metrics by Bergman metrics is also discussed.
LA - eng
UR - http://eudml.org/doc/10602
ER -

References

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