B. Ammann

activity

19982005

most citedThe smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions

12 citations · 15 across the 3 of their papers we have counts for

collaborators

8 papers

math.DG2005

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…

math.DG2003★ 12 cited

The smallest Dirac eigenvalue in a spin-conformal class and cmc-immersions

Bernd Ammann

Let us fix a conformal class $[g_{0}]$ and a spin structure $σ$ on a compact manifold $M$ . For any $g \in [g_{0}]$ , let $λ_{1}^{+} (g)$ be the smallest positive eigenvalue of the Dirac opera…

math.OA2002★ 3 cited

Complex powers and non-compact manifolds

Bernd Ammann, Robert Lauter, Victor Nistor +1

We study the complex powers $A^{z}$ of an elliptic, strictly positive pseudodifferential operator $A$ using an axiomatic method that combines the approaches of Guillemin and Seeley…

math.DG2001

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…

math.DG1999

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 $\int_{T^{2}} H^{2} \geq 2 π^{2}$ . We prove it under the condition that the…

math.DG1998

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.