Conformal geometry, contact geometry, and the calculus of variations

@article{Viaclovsky2000ConformalGC,
  title={Conformal geometry, contact geometry, and the calculus of variations},
  author={Jeff A. Viaclovsky},
  journal={Duke Mathematical Journal},
  year={2000},
  volume={101},
  pages={283-316}
}
for metricsg in the conformal class of g0, where we use the metric g to view the tensor as an endomorphism of the tangent bundle and where σk d notes the trace of the induced map on the kth exterior power; that is, σk is the kth elementary symmetric function of the eigenvalues. The case k = 1,R = constant is known as the Yamabe problem, and it has been studied in great depth (see [11] and [17]). We let M1 denote the set of unit volume metrics in the conformal class [g0]. We show that these… Expand

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