# A Monge-Ampère equation in conformal geometry

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

- Volume: 7, Issue: 2, page 241-270
- ISSN: 0391-173X

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topGursky, Matthew J.. "A Monge-Ampère equation in conformal geometry." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.2 (2008): 241-270. <http://eudml.org/doc/272266>.

@article{Gursky2008,

abstract = {We consider the Monge-Ampère-type equation $\det (A + \lambda g) = \mathrm \{const\}.$, where $A$ is the Schouten tensor of a conformally related metric and $\lambda > 0$ is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique.},

author = {Gursky, Matthew J.},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

keywords = {Monge-Ampère equation; -Yamabe problem; conformal geometry; nonlinear equations},

language = {eng},

number = {2},

pages = {241-270},

publisher = {Scuola Normale Superiore, Pisa},

title = {A Monge-Ampère equation in conformal geometry},

url = {http://eudml.org/doc/272266},

volume = {7},

year = {2008},

}

TY - JOUR

AU - Gursky, Matthew J.

TI - A Monge-Ampère equation in conformal geometry

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

PY - 2008

PB - Scuola Normale Superiore, Pisa

VL - 7

IS - 2

SP - 241

EP - 270

AB - We consider the Monge-Ampère-type equation $\det (A + \lambda g) = \mathrm {const}.$, where $A$ is the Schouten tensor of a conformally related metric and $\lambda > 0$ is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique.

LA - eng

KW - Monge-Ampère equation; -Yamabe problem; conformal geometry; nonlinear equations

UR - http://eudml.org/doc/272266

ER -

## References

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