The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.
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Jean-Michel Bismut (1986)
Inventiones mathematicae
Robert Brooks (1985)
Journal für die reine und angewandte Mathematik
H. Kumagai (1999)
Acta Arithmetica
Harold Donnelly (1980/1981)
Manuscripta mathematica
Bernd Ammann (1997/1998)
Séminaire de théorie spectrale et géométrie
D. G. Vassiliev (1991/1992)
Séminaire Équations aux dérivées partielles (Polytechnique)
Hozo, Iztok (1995)
The Electronic Journal of Combinatorics [electronic only]
Peter B. Gilkey, Boris Botvinnik (1995)
Mathematische Annalen
Brooks, Robert, Makover, Eran (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Yingbo Han, Shuxiang Feng (2011)
Archivum Mathematicum
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.
Hajime Urakawa (1986)
Compositio Mathematica
H. Englisch, M. Schröder, P. Šeba (1987)
Annales de l'I.H.P. Physique théorique
Robert Brooks (1981)
Commentarii mathematici Helvetici
Haizhong Li, Linlin Su (2005)
Banach Center Publications
We obtain inequalities between the eigenvalues of the Schrödinger operator on a compact domain Ω of a submanifold M in with boundary ∂Ω, which generalize many existing inequalities for the Laplacian on a bounded domain of a Euclidean space. We also establish similar inequalities for a closed minimal submanifold in the unit sphere, which generalize and improve Yang-Yau’s result.
P. Buser, K.-D. Semmler (1988)
Commentarii mathematici Helvetici
Jürgen Eichhorn (1991)
Archivum Mathematicum
Nakad, Roger (2011)
Advances in Mathematical Physics
Pierre Guerini, Alessandro Savo (2002/2003)
Séminaire de théorie spectrale et géométrie
Carolyn Gordon, D. DeTurck, H. Gluck (1993)
Inventiones mathematicae
Peter A. Perry (1989)
Journal für die reine und angewandte Mathematik
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