Conformal deformations of the smallest eigenvalue of the Ricci tensor

  title={Conformal deformations of the smallest eigenvalue of the Ricci tensor},
  author={P. Guan and P. Wang},
  journal={American Journal of Mathematics},
  pages={499 - 526}
  • P. Guan, P. Wang
  • Published 2005
  • Mathematics
  • American Journal of Mathematics
  • We consider deformations of metrics in a given conformal class such that the smallest eigenvalue of the Ricci tensor is a constant. It is related to the notion of minimal volumes in comparison geometry. Such a metric with the smallest eigenvalue of the Ricci tensor to be a constant is an extremal metric of volume in a suitable sense in the conformal class. The problem is reduced to solve a Pucci type equation with respect to the Schouten tensor. We establish a local gradient estimate for this… CONTINUE READING
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