First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow
Abstract
Full text article
References
J. P. Bourguignon, Ricci curvature and Einstein metrics, Global differential geometry and global analysis (Berlin,1979) Lecture nots in Math. vol. 838, Springer, Berlin, 1981, 42-63.
X. D. Cao, Eigenvalues of $(-Delta+frac{R}{2})$ on manifolds with nonnegative curvature operator. Math. Ann. 337 (2) (2007), 435-441.
X. D. Cao, First eigenvalues of geometric operators under the Ricci flow, Proc. Amer. Math. Soc. 136 (2008), 4075-4078.
G. Catino, L. Cremaschi, Z. Djadli, C. Mantegazza, L. Mazzieri, The Ricci-Bourguignon flow, Pacific J. Math. (2015).
L. F. D. Cerbo, Eigenvalues of the Laplacian under the Ricci flow, Rendiconti di Mathematica, Serie VII, Volume
, Roma (2007), 183-195.
Q. -M. Cheng and H. C. Yang, Estimates on eigenvalues of Laplacian, Math. Ann., 331 (2005),
-460.
S. Fang and F. Yang, First eigenvalues of geometric operators under the Yamabe flow, Bull. Korean Math. Soc. 53 (2016), 1113-1122.
J. F. Li, Eigenvalues and energy functionals with monotonicity formula under Ricci flow, Math. Ann. (2007) 338,
-946.
G. Perelman, The entropy formula for the Ricci flow and its geometric applications (2002), ArXiv: 0211159.
F. S. Wen, X. H. Feng, Z. Peng, Evolution and monotonicity of eigenvalues under the Ricci flow, Sci. China Math. 58 (2015),no. 8, 1737-1744.
J. Y. Wu, First eigenvalue monotonicity for the $p$-Laplace operator under the Ricci flow,
Acta mathematica Sinica, English senes, Vol. 27, NO.8 (2011), 1591-1598.
F. Zeng, Q. He, B. Chen, Monotonicity of eigenvalues of geometric operators along the Ricci-Bourguignon flow, Arxiv, 152.08158v1.