Energy functionals for Calabi-Yau metrics

Advances in Theoretical and Mathematical Physics

Volumn 17, Issue 5, 2013, Pages 867-902

  Headrick, Matthew ^a   Nassar, Ali ^b  

^a BRANDEIS UNIVERSITY   (United States)

^b Zewail City of Science and Technology   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84901492044     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: 10.4310/ATMP.2013.v17.n5.a1     Document Type: Article

References (17)

1. M. Headrick and T. Wiseman, Numerical Ricci-flat metrics on K3, Classical Quantum Gravity 22 (2005), 4931-4960; arXiv: hep-th/ 0506129.
2. S.K. Donaldson, Some numerical results in complex differential geometry, Pure Appl. Math. Q. 5(2 part 1) (2009), 571-618.
3. M.R. Douglas, R.L. Karp, S. Lukic and R. Reinbacher, Numerical solution to the Hermitian Yang-Mills equation on the Fermat quintic, J. High Energy Phys. 12 (2007), 083, arXiv: hep-th/0606261.
4. M.R. Douglas, R.L. Karp, S. Lukic and R. Reinbacher, Numerical Calabi-Yau metrics, J. Math. Phys. 49 (2008), 032302, arXiv: hep-th/ 0612075.
5. V. Braun, T. Brelidze, M.R. Douglas and B.A. Ovrut, Calabi-Yau metrics for quotients and complete intersections, J. High Energy Phys. 05 (2008), 080, arXiv: 0712.3563.
6. V. Braun, T. Brelidze, M.R. Douglas and B.A. Ovrut, Eigenvalues and eigenfunctions of the scalar Laplace operator on Calabi-Yau manifolds, J. High Energy Phys. 07 (2008), 120, arXiv: 0805.3689.
7. J. Keller and S. Lukic, Numerical Weil-Petersson metrics on moduli spaces of Calabi-Yau manifolds, 2009, arXiv: 0907.1387 [math.DG].
8. C. Doran, M. Headrick, C.P. Herzog, J. Kantor and T. Wiseman, Numerical Kaehler-Einstein metric on the third del Pezzo, Commun. Math. Phys. 282 (2008), 357-393, arXiv: hep-th/0703057.
9. J. Keller, Ricci iterations on Kähler classes, J. Inst. Math. Jussieu 8(4) (2009), 743-768, arXiv: 0709.1490.
10. R.S. Bunch and S.K. Donaldson, Numerical approximations to extremal metrics on toric surfaces, in 'Handbook of geometric analysis, Adv. Lect. Math. (ALM)', Int. Press, Somerville, MA, No. 1, vol. 7, 2008, pp. 1-28.
11. M.R. Douglas and S. Klevtsov, Black holes and balanced metrics, 2008, arXiv: 0811.0367.
12. W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical recipes: the art of scientific computing, Cambridge University Press, New York, NY, USA, 3 ed., 2007.
13. E. Calabi, Extremal Kählermetrics, Seminar on Differential Geometry, Ann. Math. Stud., 102 pp. 259-290. Princeton University Press, Princeton, N.J., 1982.
14. T. Mabuchi, K-energy maps integrating Futaki invariants, Tohoku Math. J. (2) 38(4) (1986), 575-593.
15. R.J. Berman, S. Boucksom, V. Guedj and A. Zeriahi, A variational approach to complex Monge-Ampére equations, 2009, arXiv: 0907.4490.
16. D. Baumann, A. Dymarsky, S. Kachru, I.R. Klebanov and L. McAllister, D3-brane potentials from fluxes in AdS/CFT, 2010, arXiv: 1001.5028.
17. G. Perelman, The entropy formula for the Ricci flow and its geometric applications, 2002, arXiv: math/0211159.