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Award ID contains: 1908513

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  1. ; (, Journal of the London Mathematical Society)
    Abstract In this paper, we prove sharp decay estimates of nonnegative generalized subharmonic functions on graphs with positive Laplacian spectrum, which extends the result by Li and Wang (J. Differential Geom. 58 (2001) 501–534) on Riemannian manifolds. 
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  2. ; (, The Journal of Geometric Analysis)
    Full Text Available 
  3. ; (, Contemporary mathematics)
    In this short article, we explore some basic results associated to the Generalized Weyl criterion for the essential spectrum of the Laplacian on Riemannian manifolds. We use the language of Gromov-Hausdorff convergence to recall a spectral gap theorem. Finally, we make the necessary adjustments to extend our main results, and construct a class of complete noncompact manifolds with an arbitrarily large number of gaps in the spectrum of the Hodge Laplacian acting on differential forms. 
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    Accepted Manuscript Full Text Available
  4. ; (, Contemprory Mathematics)
    In this short article, we explore some basic results associated to the Generalized Weyl criterion for the essential spectrum of the Laplacian on Riemannian manifolds. We use the language of Gromov-Hausdorff convergence to recall a spectral gap theorem. Finally, we make the necessary adjustments to extend our main results, and construct a class of complete noncompact manifolds with an arbitrarily large number of gaps in the spectrum of the Hodge Laplacian acting on differential forms. 
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    Accepted Manuscript Full Text Available
  5. ; ; (, The Journal of Geometric Analysis)
    Full Text Available 
  6. ; ; (, Journal of Mathematical Physics)
    We show that non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum. This extends our previous result [Hezari et al., Ann. Henri Poincare 18(12), 3759–3792 (2017)], which was only concerned with the Neumann Laplace spectrum. 
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  7. ; ; ; (, Linear Algebra and its Applications)
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  8. ; ; (, Contemporary mathematics)
    null; null; null; null; null; null (Ed.)
    In this short note, we survey some basic results related to the New Weyl criterion for the essential spectrum. We then use the language of Gromov-Hausdorff convergence to prove a spectral gap theorem. 
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    Full Text Available