scholarly journals Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator

2012 ◽  
Vol 2 (1) ◽  
pp. 1-56 ◽  
Author(s):  
Rafael D. Benguria ◽  
Helmut Linde ◽  
Benjamín Loewe
Keyword(s):  
Schrödinger Operator ◽  
Isoperimetric Inequalities ◽  
Schrodinger Operator ◽  
Eigenvalues Of The Laplacian

scholarly journals Geometric and spectral estimates based on spectral Ricci curvature assumptions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Gilles Carron ◽  
Christian Rose
Keyword(s):  
Fundamental Group ◽  
Ricci Curvature ◽  
Schrödinger Operator ◽  
Ricci Tensor ◽  
Isoperimetric Inequalities ◽  
Spectral Condition ◽  
Schrodinger Operator ◽  
Spectral Estimates ◽  
Finite Fundamental Group ◽  
Lowest Eigenvalue

AbstractWe obtain a Bonnet–Myers theorem under a spectral condition: a closed Riemannian {(M^{n},g)} manifold for which the lowest eigenvalue of the Ricci tensor ρ is such that the Schrödinger operator {\Delta+(n-2)\rho} is positive has finite fundamental group. Further, as a continuation of our earlier results, we obtain isoperimetric inequalities from Kato-type conditions on the Ricci curvature. We also obtain the Kato condition for the Ricci curvature under purely geometric assumptions.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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