An upper bound for the first eigenvalue of the Dirac operator on compact spin manifolds

1991 ◽  
Vol 206 (1) ◽  
pp. 409-422 ◽  
Author(s):  
Helga Baum
Keyword(s):  
Dirac Operator ◽  
Upper Bound ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Spin Manifolds

scholarly journals Sharp upper bound for the first eigenvalue

2013 ◽  
Vol 169 (1) ◽  
pp. 397-410 ◽  
Author(s):  
Raveendran Binoy ◽  
G. Santhanam
Keyword(s):  
Upper Bound ◽  
First Eigenvalue ◽  
The First Eigenvalue

scholarly journals THE FIRST EIGENVALUE OF THE DIRAC OPERATOR IN A CONFORMAL CLASS

2006 ◽  
Vol 03 (05n06) ◽  
pp. 833-844 ◽  
Author(s):  
BERND AMMANN ◽  
EMMANUEL HUMBERT
Keyword(s):  
Dirac Operator ◽  
Variational Problem ◽  
Mean Curvature ◽  
Unit Volume ◽  
Constant Mean Curvature ◽  
Positive Eigenvalue ◽  
First Eigenvalue ◽  
Conformal Class ◽  
Open Problems ◽  
The First Eigenvalue

In this overview article, we study the first positive eigenvalue of the Dirac operator in a unit volume conformal class. In particular, we discuss the question whether the infimum is attained. In the first part, we explain the corresponding variational problem. In the following parts we discuss the relation to the spinorial mass endomorphism and an application to surfaces of constant mean curvature. The article also mentions some open problems and work in progress.

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