Geodesic
Evolution of Eigenvalues along Rescaled Ricci Flow
Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 127-135

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we discuss monotonicity formulae of various entropy functionals under various rescaled versions of Ricci flow. As an application, we prove that the lowest eigenvalue of a family of geometric operators $-4\Delta \,+\,kR$ is monotonic along the normalized Ricci flow for all $k\,\ge \,1$ provided the initial manifold has nonpositive total scalar curvature.
DOI : 10.4153/CMB-2011-162-6
Mots-clés : 58C40, 53C44, monotonicity formulas, Ricci flow 
Li, Junfang. Evolution of Eigenvalues along Rescaled Ricci Flow. Canadian mathematical bulletin, Tome 56 (2013) no. 1, pp. 127-135. doi: 10.4153/CMB-2011-162-6
@article{10_4153_CMB_2011_162_6,
     author = {Li, Junfang},
     title = {Evolution of {Eigenvalues} along {Rescaled} {Ricci} {Flow}},
     journal = {Canadian mathematical bulletin},
     pages = {127--135},
     year = {2013},
     volume = {56},
     number = {1},
     doi = {10.4153/CMB-2011-162-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-162-6/}
}
TY  - JOUR
AU  - Li, Junfang
TI  - Evolution of Eigenvalues along Rescaled Ricci Flow
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 127
EP  - 135
VL  - 56
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-162-6/
DO  - 10.4153/CMB-2011-162-6
ID  - 10_4153_CMB_2011_162_6
ER  - 
%0 Journal Article
%A Li, Junfang
%T Evolution of Eigenvalues along Rescaled Ricci Flow
%J Canadian mathematical bulletin
%D 2013
%P 127-135
%V 56
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-162-6/
%R 10.4153/CMB-2011-162-6
%F 10_4153_CMB_2011_162_6

[1] [1] Akutagawa, K., Ishida, M., and LeBrun, C., Perelman's invariant, Ricci flow, and the Yamabe invariants of smooth manifolds. Arch. Math. 88 (2007), no. 1, 71–76. Google Scholar

[2] [2] Cao, X., Eigenvalues of(-Δ R/2 ) on manifolds with nonnegative curvature operator. Math. Ann. 337 (2007), no. 2, 435–441. Google Scholar

[3] [3] Cao, X., First eigenvalues of geometric operators under Ricci flow. arxiv:math.DG/0710.3947v1. Google Scholar

[4] [4] Chow, B. and Knopf, D., The Ricci Flow: An Introduction. Mathematical Surveys and Monographs 110. American Mathematical Society, Providence, RI, 2004. Google Scholar

[5] [5] Chow, B., S.-C. Chu, Glickenstein, D., et al., The Ricci Flow: Techniques and Applications. Part I. Geometric Aspects. Mathematical Surveys and Monographs 135. American Mathematical Society, Providence, RI, 2007. Google Scholar

[6] [6] Hamilton, R. S., The formation of singularities in the Ricci flow. In: Surveys in Differential Geometry, Vol. II. Internat. Press, Cambridge, MA, 1995, pp. 7–136. Google Scholar

[7] [7] Ivey, T., Ricci solitons on compact three-manifolds. Differential Geom. Appl. 3 (1993), no. 4, 301–307. Google Scholar | DOI

[8] [8] Li, J.-F., Eigenvalues and energy functionals with monotonicity formulae under Ricci flow. Math. Ann. 338 (2007), 927–946. Google Scholar | DOI

[9] [9] Oliynyka, T., Suneetab, V., and E.Woolgara, Irreversibility of world-sheet renormalization group flow. Phys. Lett. B,610 (2005), no. 1-2, 115–121. Google Scholar | DOI

[10] [10] Perelman, G., The entropy formula for the Ricci flow and its geometric applications. arxiv:math.DG/0211159. Google Scholar

Cité par Sources :