A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

@article{Li1982ANC,
  title={A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces},
  author={Peter Li and Shing-Tung Yau},
  journal={Inventiones mathematicae},
  year={1982},
  volume={69},
  pages={269-291}
}
  • Peter Li, S. Yau
  • Published 1 June 1982
  • Mathematics
  • Inventiones mathematicae
Let M be a compact Riemannian manifold with a fixed conformal structure. Then we introduce the concept of conformal volume of M in the following manner. For each branched conformal immersion q9 of M into the unit sphere S n, we consider the set of all branched conformal immersions obtained by composi t ion of qo with the conformal automorphisms of S". We let Vc(n, qg) be the max imum volume of these branched immersions. The conformal volume of M is defined to be the infimum of V.(n, q0) where… 
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