Geodesic
Liouville theorems for self-similar solutions of heat flows
Journal of the European Mathematical Society, Tome 11 (2009) no. 1, pp. 207-221 Cet article a éte moissonné depuis la source EMS Press

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Let N be a compact Riemannian manifold. A quasi-harmonic sphere is a harmonic map from (Rm,e−∣x∣2/2(m−2)ds02​) to N (m≥3) with finite energy ([LnW]). Here ds02​ is the Euclidean metric in Rm. It arises from the blow-up analysis of the heat flow at a singular point. In this paper, we prove some kinds of Liouville theorems for the quasi-harmonic spheres. It is clear that the Liouville theorems imply the existence of the heat flow to the target N. We also derive gradient estimates and Liouville theorems for positive quasi-harmonic functions.
DOI : 10.4171/jems/147
Classification : 35-XX, 58-XX, 00-XX
Keywords: Harmonic sphere, self-similar solution, quasi-harmonic sphere, heat flow 
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     author = {Jiayu Li and Meng Wang},
     title = {Liouville theorems for self-similar solutions of heat flows},
     journal = {Journal of the European Mathematical Society},
     pages = {207--221},
     year = {2009},
     volume = {11},
     number = {1},
     doi = {10.4171/jems/147},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/147/}
}
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Jiayu Li; Meng Wang. Liouville theorems for self-similar solutions of heat flows. Journal of the European Mathematical Society, Tome 11 (2009) no. 1, pp. 207-221. doi: 10.4171/jems/147

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