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Some local eigenvalue estimates involving curvatures

  • Mouhamed Moustapha FallEmail author
Article

Abstract

We first establish a local Faber–Krahn isoperimetric comparison in terms of scalar curvature pinching. Secondly we derive estimates of Cheeger constants related to the Dirichlet and Neumann problems via the (relative) isoperimetric profiles which allow us to obtain, in particular, lower bounds for first non-zero eigenvalues of the problem of Dirichlet and Neumann. These estimates involve scalar curvature and mean curvature respectively.

Mathematics Subject Classification (2000)

15A42 35B05 35R45 52A40 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.SissaTriesteItaly

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