Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The behavior of the Chern scalar curvature under the Chern-Ricci flow


Authors: Matthew Gill and Daniel Smith
Journal: Proc. Amer. Math. Soc. 143 (2015), 4875-4883
MSC (2010): Primary 53C44; Secondary 53C55
DOI: https://doi.org/10.1090/proc/12745
Published electronically: June 16, 2015
MathSciNet review: 3391045
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study finite-time singularities in the Chern-Ricci flow. We show that finite-time singularities are characterized by the blow-up of the scalar curvature of the Chern connection.


References [Enhancements On Off] (What's this?)

  • [1] T. Collins and V. Tosatti, Kähler currents and null loci, ArXiv e-prints (2013).
  • [2] Matt Gill, Convergence of the parabolic complex Monge-Ampère equation on compact Hermitian manifolds, Comm. Anal. Geom. 19 (2011), no. 2, 277-303. MR 2835881 (2012h:32047), https://doi.org/10.4310/CAG.2011.v19.n2.a2
  • [3] Ke-Feng Liu and Xiao-Kui Yang, Geometry of Hermitian manifolds, Internat. J. Math. 23 (2012), no. 6, 1250055, 40. MR 2925476, https://doi.org/10.1142/S0129167X12500553
  • [4] Morgan Sherman and Ben Weinkove, Local Calabi and curvature estimates for the Chern-Ricci flow, New York J. Math. 19 (2013), 565-582. MR 3119098
  • [5] Jian Song and Ben Weinkove, An introduction to the Kähler-Ricci flow, An introduction to the Kähler-Ricci flow, Lecture Notes in Math., vol. 2086, Springer, Cham, 2013, pp. 89-188. MR 3185333, https://doi.org/10.1007/978-3-319-00819-6_3
  • [6] Jeffrey Streets and Gang Tian, A parabolic flow of pluriclosed metrics, Int. Math. Res. Not. IMRN 16 (2010), 3101-3133. MR 2673720 (2011h:53091), https://doi.org/10.1093/imrn/rnp237
  • [7] Jeffrey Streets and Gang Tian, Hermitian curvature flow, J. Eur. Math. Soc. (JEMS) 13 (2011), no. 3, 601-634. MR 2781927 (2012f:53142), https://doi.org/10.4171/JEMS/262
  • [8] Valentino Tosatti and Ben Weinkove, On the evolution of a Hermitian metric by its Chern-Ricci form, J. Differential Geom. 99 (2015), no. 1, 125-163. MR 3299824
  • [9] V. Tosatti, B. Weinkove, and X. Yang, Collapsing of the Chern-Ricci flow on elliptic surfaces, ArXiv e-prints (2013).
  • [10] Valentino Tosatti and Ben Weinkove, The Chern-Ricci flow on complex surfaces, Compos. Math. 149 (2013), no. 12, 2101-2138. MR 3143707, https://doi.org/10.1112/S0010437X13007471
  • [11] Zhou Zhang, Scalar curvature behavior for finite-time singularity of Kähler-Ricci flow, Michigan Math. J. 59 (2010), no. 2, 419-433. MR 2677630 (2011j:53128), https://doi.org/10.1307/mmj/1281531465

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 53C44, 53C55

Retrieve articles in all journals with MSC (2010): 53C44, 53C55


Additional Information

Matthew Gill
Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall #3840, Berkeley, California 94720-3840

Daniel Smith
Affiliation: Department of Mathematics, Furman University, 3300 Poinsett Highway, Greenville, South Carolina 29613

DOI: https://doi.org/10.1090/proc/12745
Received by editor(s): February 7, 2014
Received by editor(s) in revised form: July 27, 2014
Published electronically: June 16, 2015
Additional Notes: This research was supported by NSF RTG grant DMS-0838703.
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society