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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
DOI: https://doi.org/10.1090/S0002-9947-03-03307-5
Published electronically: April 17, 2003
MathSciNet review: 1974691
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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] Audin, M., The topology of torus actions on symplectic manifolds, Progress in Math., vol. 93, Birkhäuser-Verlag, Basel, 1991 MR 92m:57046
  • [F] Futaki, A., The Ricci curvature of symplectic quotients of Fano manifolds, Tohoku Math. J., 39 (1987), 329-339 MR 88m:53124
  • [G] Goldstein, E., Minimal Lagrangian tori in Kaehler Einstein manifolds, math.DG/0007135 (preprint)
  • [H] Hsiang, W., On the compact homogeneous minimal submanifolds, Proc. Nat. Acad. Sci., 56 (1966), pp. 5-6 MR 34:5037
  • [HL] Hsiang, W. and Lawson, H. B., Jr., Minimal submanifolds of low cohomogeneity, J. Differential Geometry, 5 (1971), pp. 1-38 MR 45:7645
  • [K1] Kobayashi, S., Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, 1972 MR 50:8360
  • [K2] Kobayashi, S., On compact Kaehler manifolds with positive definite Ricci tensor, Ann. of Math. (2), 74 (1961), pp. 570-574 MR 24:A2922
  • [TY] Thomas, R. and Yau, S.-T., Special Lagrangians, stable bundles and mean curvature flow, math.DG/0104197 (preprint)

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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
Email: pacini@paley.dm.unipi.it, pacini@math.gatech.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03307-5
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

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