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  • P-ISSN3059-0604
  • E-ISSN3059-1309
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ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 18(1), 79-86, https://doi.org/10.7468/jksmeb.2011.18.1.079

Abstract

Suppose that (M,g) is a complete and noncompact Riemannian mani-fold with Ricci curvature bounded below by $-K{\leq}0$ and (N, $\bar{g}$) is a complete Riemannian manifold with nonpositive sectional curvature. Let u : $M{\times}[0,{\infty}){\rightarrow}N$ 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: Theoretical Mathematics and Pedagogical Mathematics

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