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

  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},
  • 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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L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
Soit M n une sous-variete a n dimensions immergee de facon minimale de M n+l , l>1. Soit D⊂M un domaine compact. On demontre des theoremes de comparaisons pour les noyaux de la chaleur H(x, y, t) et
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© Foundation Compositio Mathematica, 1973, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions
On the total curvature of immersed manifolds. II.
Sur les premi6res valeurs propres des vari6t6s riemanniennes
  • Compositio Math. 26,
  • 1973
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