A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations
Naito, Hisashi
Compositio Mathematica, Tome 68 (1988), p. 221-239 / Harvested from Numdam
Publié le : 1988-01-01
@article{CM_1988__68_2_221_0,
     author = {Naito, Hisashi},
     title = {A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations},
     journal = {Compositio Mathematica},
     volume = {68},
     year = {1988},
     pages = {221-239},
     mrnumber = {966581},
     zbl = {0669.35049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1988__68_2_221_0}
}
Naito, Hisashi. A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations. Compositio Mathematica, Tome 68 (1988) pp. 221-239. http://gdmltest.u-ga.fr/item/CM_1988__68_2_221_0/

1 Th. Aubin: Nonlinear analysis on manifolds, Monge-Amperé equations. Springer-Verlag, Berlin-Heiderberg -New York (1983). | MR 681859 | Zbl 0512.53044

2 N. Chafee and E. Infant: A bifurcation problem for a nonlinear parabolic equation. J. Appl. Anal. 4 (1974) 17-37. | MR 440205 | Zbl 0296.35046

3 J. Eells and L. Lemaire: Selected topics in harmonic maps. C.B.M.S. Regional Conference Series in Math. Vol. 50, (1983). | MR 703510 | Zbl 0515.58011

4 J. Eells and J.H. Sampson: Variational theory in fiber bundles. Proc. U.S. Japan Seminar in Diff. Geom. (1965) pp. 22-33. | MR 216519 | Zbl 0192.29801

5 J. Eells and J.H. Sampson: Harmonic mapping of Riemannian manifolds. Amer. J. Math. 86 (1964) 109-160. | MR 164306 | Zbl 0122.40102

6 C.L. Epstein and M.I. Weinstein: A stable manifold theorem for the curve shortening equation. Comm. Pure Appl. Math. 40 (1987) 119-139. | MR 865360 | Zbl 0602.34026

7 D. Gillberg and N.S. Trudinger: Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin-Heiderberg -New York (1983). | MR 737190 | Zbl 0562.35001

8 M. Gage And R.S. Hamilton: The equation shrinking convex plain curves. J. Diff. Geom. 23 (1986) 69-96. | MR 840401 | Zbl 0621.53001

9 D. Henry: Geometric Theory of Semilinear Parabolic Equations. L.N.M. 840, Springer-Verlag, Berlin-Heiderberg- New York (1981). | MR 610244 | Zbl 0456.35001

10 R.S. Hamilton: Harmonic Maps of Manifolds with Boundary. L.N.M. 471, Springer-Verlag, Berlin-Heiderberg- New York (1975). | MR 482822 | Zbl 0308.35003

11 R. Palais: Foundations in Non-linear Global Analysis, Benjamin. New York (1967). | Zbl 0164.11102

12 I. Mogi and M. Ito: Differential Geometry and Gauge Theory (in Japanese). Kyoritsu, Tokyo (1986).

13 H. Naito: Asymptotic behavior of solutions to Eells-Sampson equations near stable harmonic maps. preprint. | MR 1017578 | Zbl 0688.58007

14 H. Naito: Asymptotic behavior of non-linear heat equations in geometric variational problems. preprint.

15 L. Simon: Asymptotic for a class of non-linear evolution equations, with applications to geometric problem. Ann. of Math. 118 (1983) 525-571. | Zbl 0549.35071

16 L. Simon: Asymptotic behaviour near isolated singular points for geometric variational problems. Proc. Centre for Math. Anal., Australian National University, (Proceeding of Miniconference on Geometry and Partial Differential Equations) Vol. 10 (1985) pp. 1-7. | MR 857649 | Zbl 0606.58016