Explicit Yamabe Flow of an Asymmetric Cigar
Burchard, Almut ; McCann, Robert J. ; Smith, Aaron
Methods Appl. Anal., Tome 15 (2008) no. 1, p. 65-80 / Harvested from Project Euclid
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We consider the Yamabe flow of a conformally Euclidean manifold for which the conformal factor’s reciprocal is a quadratic function of the Cartesian coordinates at each instant in time. This leads to a class of explicit solutions having no continuous symmetries (no Killing fields) but which converge in time to the cigar soliton (in two-dimensions, where the Ricci and Yamabe flows coincide) or in higher dimensions to the collapsing cigar. We calculate the exponential rate of this convergence precisely, using the logarithm of the optimal bi-Lipschitz constant to metrize distance between two Riemannian manifolds.
Publié le : 2008-03-15
Classification:  Exact Yamabe flows,  Ricci flow,  conformally flat non-compact manifold,  quadratic conformal factor,  cigar soliton,  attractor,  basin of attraction,  rate of convergence,  Lyapunov exponent,  biLipschitz,  53C44,  35K55,  58J35 
@article{1228920873,
     author = {Burchard, Almut and McCann, Robert J. and Smith, Aaron},
     title = {Explicit Yamabe Flow of an Asymmetric Cigar},
     journal = {Methods Appl. Anal.},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 65-80},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1228920873}
}

Burchard, Almut; McCann, Robert J.; Smith, Aaron. Explicit Yamabe Flow of an Asymmetric Cigar. Methods Appl. Anal., Tome 15 (2008) no. 1, pp.  65-80. http://gdmltest.u-ga.fr/item/1228920873/