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 APM  Vol.7 No.1 , January 2017
RETRACTED: Eigenvalues of the p-Laplacian and Evolution under the Ricci-Harmonic Map Flowc
Paul Bracken
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Abstract: Short Retraction Notice  The paper does not meet the standards of "Advances in Pure Mathematics". This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.  Please see the article page for more details. The full retraction notice in PDF is preceding the original paper which is marked "RETRACTED".
Keywords: Manifold, Operators, p-Laplacian, Eigenvalues
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References

[1]   Chow, B., Lu, P. and Ni, L. (2006) Hamilton’s Ricci Flow, AMS Graduate Studies in Mathematics, 77, Providence, RI.

[2]   Wu, J. (2011) First Eigenvalue Monotonicity for the p-Laplacian Operator under the Ricci Flow. Acta Mathematica Sinica, 27, 1591-1598.

[3]   Perelman, G. (2002) The Entropy Formula for the Ricci Flow and Its Geometric Application. arXiv: math.DG/0211159v1

[4]   Lee, J.M. (2009) Manifolds and Differential Geometry, AMS Graduate Studies in Mathematics, Volume 107, Providence, RI.
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[5]   Chow, B. (1991) The Ricci flow on the 2-Sphere. Journal of Differential Geometry, 33, 325-334.

[6]   Cao, X. (2007) Eigenvalues of on Manifolds with Nonnegative Curvature Operator. Mathematische Annalen, 337, 435-441.
https://doi.org/10.1007/s00208-006-0043-5

[7]   Cao, X. (2008) First Eigenvalues of Geometric Operators under the Ricci Flow. Proceedings of American Mathematical Society, 136, 4075-4078.
https://doi.org/10.1090/S0002-9939-08-09533-6

[8]   Abolarinwa, A. (2015) Evolution and Monotonicity of the First Eigenvalue of p-Laplacian under the Ricci-Harmonic Flow. Journal of Applied Analysis, 21, 147-174.
https://doi.org/10.1515/jaa-2015-0013

 
 
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