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Sharp gradient estimates for eigenfunctions on Riemannian manifolds

Published online by Cambridge University Press:  17 April 2009

Albert Borbély
Albert Borbély
Affiliation:
Department of Mathematics and Computer ScienceKuwait UniversityPO Box 5969Safat 13060Kuwait
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Abstract

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Sharp gradient estimates are derived for positive eigenfunctions on complete Riemannian manifolds with Ricci curvature bounded below.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 253 - 259
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Gallot, S., Hulin, D. and Lafontaine, J., Riemannian geometry (Springer-Verlag, Berlin, Heidelberg, New York, 1993).Google Scholar
[2]Yau, S.T., ‘Harmonic functions on complete Riemannian manifolds’, Comm. Pure Appl. Math. 28 (1975), 201–228.CrossRefGoogle Scholar