Ambient Dirac eigenvalue estimates and the Willmore functional

Bernd Ammann (1)

1 IECN - Institut Élie Cartan de Nancy

We prove a lower bound for the Willmore functional with the help spinors and the Dirac operator. As a corollary we verify the Willmore conjecture in a certain region of the spin-conformal moduli space for tori with sufficiently small $L^p$-norms of the Gauss curvature.

Mots clés: Dirac eigenvalue estimates; Willmore inequality; conformal immersion

Domaines: Géométrie différentielle [math.DG]

Bernd Ammann. Ambient Dirac eigenvalue estimates and the Willmore functional. Dirac operators: yesterday and today, 2005, France. pp.221--228. ⟨hal-00138821v2⟩