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Vol.18 No.1
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AN ENERGY DENSITY ESTIMATE OF HEAT EQUATION FOR HARMONIC MAP

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2011, v.18 no.1, pp.79-86
https://doi.org/10.7468/jksmeb.2011.18.1.079
Kim, Hyun-Jung
Kim,, H. (2011). AN ENERGY DENSITY ESTIMATE OF HEAT EQUATION FOR HARMONIC MAP. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 18(1), 79-86, https://doi.org/10.7468/jksmeb.2011.18.1.079
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Abstract

Suppose that (M,g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by <TEX>$-K{\leq}0$</TEX> and (N, <TEX>$\bar{g}$</TEX>) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : <TEX>$M{\times}[0,{\infty}){\rightarrow}N$</TEX> be the solution of a heat equation for harmonic map with a bounded image. We estimate the energy density of u.

keywords
heat equation for harmonic map, energy density, Liouville Theorem

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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