Schouten tensor equations in conformal geometry with prescribed boundary metric

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2005
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Zusammenfassung

We deform the metric conformally on a manifold with boundary. This induces a deformation of the Schouten tensor. We fix the metric at the boundary and realize a prescribed value for the product of the eigenvalues of the Schouten tensor in the interior, provided that there exists a subsolution. This problem reduces to a Monge-Amp`ere equation with gradient terms. The main issue is to obtain a priori estimates for the second derivatives near the boundary.

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Fachgebiet (DDC)
510 Mathematik
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Schouten tensor; fully nonlinear equation; conformal geometry; Dirichlet boundary value problem
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undefined / . - undefined, undefined
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ISO 690SCHNÜRER, Oliver C., 2005. Schouten tensor equations in conformal geometry with prescribed boundary metric. In: Electronic Journal of Differential Equations (EJDE), 81. eISSN 1072-6691
BibTex
@article{Schnurer2005Schou-41193,
  year={2005},
  title={Schouten tensor equations in conformal geometry with prescribed boundary metric},
  url={https://eudml.org/doc/125235},
  journal={Electronic Journal of Differential Equations (EJDE)},
  author={Schnürer, Oliver C.},
  note={Article Number: 81}
}
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