RETRACTED: Eigenvalues of the p-Laplacian and Evolution under the Ricci-Harmonic Map Flowc
Author(s)
Paul Bracken
ABSTRACT
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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.
https://doi.org/10.1090/gsm/107 [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
[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.
https://doi.org/10.1090/gsm/107 [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