|
Mean curvature flow, orbits, moment maps
Author(s):
Tommaso
Pacini
Journal:
Trans. Amer. Math. Soc.
355
(2003),
3343-3357.
MSC (2000):
Primary 53C42, 53C44;
Secondary 53D20
Posted:
April 17, 2003
Retrieve article in:
PDF DVI PostScript
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:
-
- [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)
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
Email:
pacini@paley.dm.unipi.it, pacini@math.gatech.edu
DOI:
10.1090/S0002-9947-03-03307-5
PII:
S 0002-9947(03)03307-5
Received by editor(s):
September 4, 2002
Received by editor(s) in revised form:
January 29, 2003
Posted:
April 17, 2003
Copyright of article:
Copyright
2003,
by the author
|
Comments: webmaster@ams.org