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REILLY INEQUALITIES OF ELLIPTIC OPERATORS ON CLOSED SUBMANIFOLDS

Part of: Global differential geometry Classical differential geometry

Published online by Cambridge University Press:  29 June 2009

RUSHAN WANG
RUSHAN WANG*
Affiliation:
College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, PR China (email: wangrs@mail.ahnu.edu.cn)
*
✉For correspondence; e-mail: wangrs@mail.ahnu.edu.cn
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Abstract

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Using generalized position vector fields we obtain new upper bound estimates of the first nonzero eigenvalue of a kind of elliptic operator on closed submanifolds isometrically immersed in Riemannian manifolds of bounded sectional curvature. Applying these Reilly inequalities we improve a series of recent upper bound estimates of the first nonzero eigenvalue of the Lr operator on closed hypersurfaces in space forms.

Keywords

closed submanifoldselliptic operatorr-mean curvature

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53A10: Minimal surfaces, surfaces with prescribed mean curvature

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 2 , October 2009 , pp. 335 - 346
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The author was partially supported by grant number 60804044 of the NSFC.

References

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