62
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Perelman’s Entropy for Some Families of Canonical Metrics

References

  • [Bérard-Bergery 82] L. Bérard-Bergery. Sur des Nouvelles Variétés Riemannienes d’Einstein. Publication de l’Institute Elie Cartan, Nancy, 1982.
  • [Cao 96] H.-D. Cao. “Existence of Gradient Ricci Solitons”. In Elliptic and Parabolic Methods in Geometry, pp. 1–16.A.K.Peters, 1996.
  • [Cao et al. 04] H.-D. Cao, R. S. Hamilton, andT. Ilmanen. “Gaussian Densities and Stability for Some Ricci Solitons.” arXiv:math/0404165, 2004.
  • [Chave and Valent 96] T. Chave and G. Valent. “On a Class of Compact and Non-compact Quasi-Einstein Metrics and Their Renormalizability Properties.” Nuclear Phys. B 478 (1996) 758–778.
  • [Dancer and Wang 11] A. Dancer and M. Wang. “On Ricci Solitons of cohomogeneity One.” Ann. Global Anal. Geom. 39 (2011), 259–292.
  • [Hall 11] S. J. Hall. “Computing Perelman’s ν-Functional.” Diff. Geom. Appl. 29 (2011), 426–432.
  • [Hall 13] S. J. Hall. “Quasi-Einstein Metrics on Hypersurface Families.” J. Geom. Phys. 64 (2013), 83–90.
  • [Kim and Kim 03] D.-S. Kim and Y. H. Kim. “Compact Einstein Warped Product Spaces with Nonpositive Scalar Curvature.” Proc. Amer. Math. Soc. 131 (2003), 2573–2576.
  • [Koiso 90] N. Koiso. “On Rotationally Symmetric Hamilton’s Equation for Kähler–Einstein Metrics.” InRecent Topics in Differential and Analytic Geometry, Advanced Studies in Pure Mathematics 18-I, pp. 327–337. Academic Press, 1990.
  • [Lü et al. 04] H. Lü, D. Page, and C. Pope. “New inhomogeneous Einstein Metrics on Sphere Bundles over Einstein–Kähler Manifolds.” Phys. Lett. B 593 (2004), 218–226.
  • [Page 79] D. Page. “A Compact Rotating Gravitational Instanton.” Phys. Lett. B 79 (1979), 235–238.
  • [Perelman 02] G. Perelman. “The Entropy Formula for the Ricci Flow and Its Geometric Applications.” arXiv:math/0211159v1, 2002.
  • [Rothaus 81] O. Rothaus. “Logarithmic Sobolev Inequalities and the Spectrum of Schrödinger Operators.” J. Funct. Anal. 42 (1981), 110–120.
  • [Song et al. 13] J. Song, G. Székelyhidi, and B. Weinkove. “The Kähler–Ricci Flow on Projective Bundles.” Int. Math. Res. Not. 2 (2013), 243–257.
  • [Wang and Wang 98] J. Wang and M.Wang. “Einstein Metrics on S2-Bundles.” Math. Ann. 310 (1998), 497–526.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.