A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations

Hisashi Naito

Compositio Mathematica (1988)

  • Volume: 68, Issue: 2, page 221-239
  • ISSN: 0010-437X

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Naito, Hisashi. "A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations." Compositio Mathematica 68.2 (1988): 221-239. <http://eudml.org/doc/89936>.

@article{Naito1988,
author = {Naito, Hisashi},
journal = {Compositio Mathematica},
keywords = {existence; stable and an unstable manifold; quasi-linear; closed Riemannian manifold; gradient flow; harmonic map; energy integral; Yang- Mills functional},
language = {eng},
number = {2},
pages = {221-239},
publisher = {Kluwer Academic Publishers},
title = {A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations},
url = {http://eudml.org/doc/89936},
volume = {68},
year = {1988},
}

TY - JOUR
AU - Naito, Hisashi
TI - A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 68
IS - 2
SP - 221
EP - 239
LA - eng
KW - existence; stable and an unstable manifold; quasi-linear; closed Riemannian manifold; gradient flow; harmonic map; energy integral; Yang- Mills functional
UR - http://eudml.org/doc/89936
ER -

References

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  1. 1 Th. Aubin: Nonlinear analysis on manifolds, Monge-Amperé equations. Springer-Verlag, Berlin-Heiderberg -New York (1983). Zbl0512.53044MR681859
  2. 2 N. Chafee and E. Infant: A bifurcation problem for a nonlinear parabolic equation. J. Appl. Anal.4 (1974) 17-37. Zbl0296.35046MR440205
  3. 3 J. Eells and L. Lemaire: Selected topics in harmonic maps. C.B.M.S. Regional Conference Series in Math. Vol. 50, (1983). Zbl0515.58011MR703510
  4. 4 J. Eells and J.H. Sampson: Variational theory in fiber bundles. Proc. U.S. Japan Seminar in Diff. Geom. (1965) pp. 22-33. Zbl0192.29801MR216519
  5. 5 J. Eells and J.H. Sampson: Harmonic mapping of Riemannian manifolds. Amer. J. Math.86 (1964) 109-160. Zbl0122.40102MR164306
  6. 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. Zbl0602.34026MR865360
  7. 7 D. Gillberg and N.S. Trudinger: Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin-Heiderberg -New York (1983). Zbl0562.35001MR737190
  8. 8 M. Gage and R.S. Hamilton: The equation shrinking convex plain curves. J. Diff. Geom.23 (1986) 69-96. Zbl0621.53001MR840401
  9. 9 D. Henry: Geometric Theory of Semilinear Parabolic Equations. L.N.M.840, Springer-Verlag, Berlin-Heiderberg- New York (1981). Zbl0456.35001MR610244
  10. 10 R.S. Hamilton: Harmonic Maps of Manifolds with Boundary. L.N.M.471, Springer-Verlag, Berlin-Heiderberg- New York (1975). Zbl0308.35003MR482822
  11. 11 R. Palais: Foundations in Non-linear Global Analysis, Benjamin. New York (1967). Zbl0164.11102
  12. 12 I. Mogi and M. Ito: Differential Geometry and Gauge Theory (in Japanese). Kyoritsu, Tokyo (1986). 
  13. 13 H. Naito: Asymptotic behavior of solutions to Eells-Sampson equations near stable harmonic maps. preprint. Zbl0688.58007MR1017578
  14. 14 H. Naito: Asymptotic behavior of non-linear heat equations in geometric variational problems. preprint. 
  15. 15 L. Simon: Asymptotic for a class of non-linear evolution equations, with applications to geometric problem. Ann. of Math.118 (1983) 525-571. Zbl0549.35071
  16. 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. Zbl0606.58016MR857649

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