12 citations · 15 across the 3 of their papers we have counts for
7 papers · 1 filter
Mass endomorphism and spinorial Yamabe type problems on conformally flat manifolds
Bernd Ammann, Emmanuel Humbert, Bertrand Morel
Let M be a compact manifold equipped with a Riemannian metric g and a spin structure \si. We let $λ(M,[g],\si)= \inf_{\tilde{g} \in [g]} λ_1^+(\tilde{g}) Vol(M,\tilde{g})^{1/n}$ wh…
The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions
Bernd Ammann
Let us fix a conformal class and a spin structure on a compact manifold . For any , let be the smallest positive eigenvalue of the Dirac opera…
Spectral estimates on 2-tori
Bernd Ammann
We prove upper and lower bounds for the eigenvalues of the Dirac operator and the Laplace operator on 2-dimensional tori. In particluar we give a lower bound for the first eigenval…
The Willmore Conjecture for immersed tori with small curvature integral
Bernd Ammann
The Willmore conjecture states that any immersion F:T^2 -> R^n of a 2-torus into flat euclidean space satisfies . We prove it under the condition that the…
The Dirac operator on collapsing S^1-bundles
Bernd Ammann
We study the behavior of the spectrum of the Dirac operator on collapsing S^1-bundles. Convergent eigenvalues will exist if and only if the spin structure is projectable.
A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus
Ilka Agricola, Bernd Ammann, Thomas Friedrich
We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to…