Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Mean curvature flow, orbits, moment maps

Author: Tommaso Pacini
Journal: Trans. Amer. Math. Soc. 355 (2003), 3343-3357
MSC (2000): Primary 53C42, 53C44; Secondary 53D20
Published electronically: April 17, 2003
MathSciNet review: 1974691
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a compact Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: e.g., finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for example, proves that the minimal Lagrangian orbits are isolated.

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

  • [A] Michèle Audin, The topology of torus actions on symplectic manifolds, Progress in Mathematics, vol. 93, Birkhäuser Verlag, Basel, 1991. Translated from the French by the author. MR 1106194
  • [F] Akito Futaki, The Ricci curvature of symplectic quotients of Fano manifolds, Tohoku Math. J. (2) 39 (1987), no. 3, 329–339. MR 902573, 10.2748/tmj/1178228281
  • [G] Goldstein, E., Minimal Lagrangian tori in Kaehler Einstein manifolds, math.DG/0007135 (preprint)
  • [H] Wu-yi Hsiang, On the compact homogeneous minimal submanifolds, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 5–6. MR 0205203
  • [HL] Wu-yi Hsiang and H. Blaine Lawson Jr., Minimal submanifolds of low cohomogeneity, J. Differential Geometry 5 (1971), 1–38. MR 0298593
  • [K1] Shoshichi Kobayashi, Transformation groups in differential geometry, Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70. MR 0355886
  • [K2] Shoshichi Kobayashi, On compact Kähler manifolds with positive definite Ricci tensor, Ann. of Math. (2) 74 (1961), 570–574. MR 0133086
  • [TY] Thomas, R. and Yau, S.-T., Special Lagrangians, stable bundles and mean curvature flow, math.DG/0104197 (preprint)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 53C42, 53C44, 53D20

Retrieve articles in all journals with MSC (2000): 53C42, 53C44, 53D20

Additional Information

Tommaso Pacini
Affiliation: Imperial College, London, UK; University of Pisa, Pisa, Italy
Address at time of publication: Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332

Received by editor(s): September 4, 2002
Received by editor(s) in revised form: January 29, 2003
Published electronically: April 17, 2003
Article copyright: © Copyright 2003 by the author